Probability - Everything You Need to Know. 11 New Tricks and Shortcuts, GRE, GMAT and more
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- Опубліковано 10 лют 2025
- Update: I am not available for tutoring! But still alive, :) Meanwhile, so many students have personally recommended Target Test Prep for GRE / GMAT that I asked them for a unique discount code, TestedTutor10, for this link: targettestprep... That’s right, everything you need to know for probability. And versus Or, with replacement and without, specific orders, simplifying probabilities, ratios and probability, probability formula, ‘at least’ in probability, probability and combinations, using venn diagrams for probability, independent probabilities, repeating probabilities until event occurs, letter arrangement probability. If you don’t learn something, I’ll eat my hat.
And it’s not just for GRE and GMAT students wanting probability questions and difficult probability examples, it’s for any student wanting an introduction to probability.
I offer private GRE / GMAT tutoring online at a fixed rate of $140/hr. Please get in touch via the email below, or through my tutoring website: www.gretutorlo...
Enquiries: philip@gretutorlondon.com
The GRE and GMAT are two of most used graduate exams for those seeking to study a Masters Degree or Masters in Business Administration (MBA) degree. The Graduate Record Exam and Graduate Management Admissions Test have been taken for over 50 years and are taken by approximately 600,000 and 300,000 people worldwide annually, respectively. These exams are typically taken between the ages of 18-40, by those who have completed, or are about to complete, their Bachelors Degree.
Business Enquiries: philip@gretutorlondon.com
Grateful for any support: / testedtutor If you’re now ready to get into your dream MBA program, my former student, Angel, is offering virtual private Admissions coaching. She was admitted into Harvard Business School, The Wharton School of Business, and Columbia Business School (accepted into every school she interviewed for) after graduating from UCLA with a degree in Communication. She also got 3 perfect scores on the GRE’s Analytical Writing Assessment (99th percentile).
Here is her link - linktr.ee/ange... - and you can reach her at angellinzhu@gmail.com with the subject line, “PHILIP SENT ME.”
![Quartiles, Percentiles, Quintiles, Interquartile Range, Box Plots [worked examples! Oh wow]](http://i.ytimg.com/vi/fhFDjxcOrb8/mqdefault.jpg)
![Lp. Сердце Вселенной #60 РОЖДЕНИЕ ЛОЛОЛОШКИ [Финал] • Майнкрафт](http://i.ytimg.com/vi/YoR0pAV9FVQ/mqdefault.jpg)
HI Philip! I gave my GRE today after binging your videos the past week. I had gotten a 313 (160Q, 153V) in my first attempt and got a score of 326 (170Q, 156V) today! I can't thank you enough for theses amazing videos. Those little quant tricks on mixtures, weighted averages, ratios, and probabilities helped me save so much time in my quant section today which certainly boosted my score by a lot. Thanks again for putting up so much free content for everyone to see, this definitely did the trick for me.
Wow, a perfect Quant score! Great job Sparsh and thank you for the kind words.
How many mocks you gave ?
Hi ..sparsh..I am planning to give GRE in Nov..pls guide me how to start from
@SparshJain how did you prepare for quants and verbal?
How to score 150 plus in verbal
At minute 38:15 the answer choices should read 0.10, 0.12, 0.18, 0.28 and 0.30. Well spotted ctlr9k!
I spotted that too, glad i read the comment
Hey philip! I gave my GRE Today after going through your videos. I secured 312 (161 q, 151 verbal). My score increased from 290 to 312. Thank you for your service for community.
Well done Raja!
hey raj, hw long it took u to increase 22pts
Hi Philip I just wanted to say you are the definition of work smarter not harder…I spent countless hours trying to memorize all this crap and learned way more in your videos. Your teaching style makes it easy to follow along! Thank you so much
Hey Philip! I was kind of waiting for this day when I could write a message to thank you. I gave my gre today and scored 321. I can't thank you enough!! You are the best teacher one could ask for😋😋
I recently took GRE and scored 314 (156V, 158Q, 4.5 AWA) in my first attempt. Though this is not as high score as 340, I am content as it would land me in a coveted University. I would thank Test Tutor for all the insights. Hope you make more such videos with these little but highly lucrative tricks. You are a constant impetus, and it is always quelling to watch you videos- keep up the good work 🙌
Thanks so much Ace
Thank you so much Philip sir for elucidating the whole mammoth of probability into a mere one shot video!! Not going to lie this video summarizes everything so easily that it makes you wanna solve more questions !!!! Amazing content as usual ! God bless you !
Hey, I gave my GRE exam today and scored 327 (V 159,Q 168). Although I have a maths background, your math videos really helped me brush up my topics and learn a few tricks too (weighted average trick is golden). Thanks for the help!
Well dobe my man!
I'm from India and have recently started watching your videos. Completed almost all the playlists and indeed this is the video I've been waiting for. Thank you for all the teaching & content that is utilised by millions of students around the world. I have my GRE, a month from now approx. and wish me luck. Thanks mate :)
So glad! Good luck TB!
atb
How was your Gre?
Hi Philip, I just wanted to say thank you!! Your videos are amazing and perfect to catch up on a lot of topics all at once. I got a 325. I couldn't repay you in any way, so I helped someone else who was taking the test and prayed for you. Just wanted to let you know that I'm so grateful for your work! Thanks again.
❤
Hi did you prepare only from these videos?
Man this video is probably the best of your videos
I scored 161 from the previous 151
Thanks a lot mate 😊
Happy Teacher's Day Philip !!!! . Your videos have helped me immensely in my preparation. Hoping to get a good score. You are venerated by all of us. God Bless
Thankyou very much!!, i am taking gre in 12 days, i needed exactly this.
Glad it helped and good luck Beast!
@@TheTestedTutor Thanks!!
I swear this fellow is a genius the topic I wasn’t understanding at all I learnt it in one class kudos to this fellow very underrated channel……This guy is saving lives ❤
Hello Philip, what was the final option for the independent event question? 0.3--0.12 = 0.18 doesn't equate to any of the fraction in the answer choice.
exactlyyy
I was thinking the same thing! Couldn’t find the answer online.
@@halizawilthe answer is 0.18
Did anyone get the answer? It’s 0.18 but what is the answer choice ?
Hello philip, I am coming to express my gratitude 🙏🏻 for all your videos especially the 5 weeks quant section, throughout the past 3 weeks I have been watching most of your videos, and I re-entered the gre general exam and my grade have raised for 10 points . Thank you so much for your great efforts (from Egypt 🇪🇬)
Hey Philip! I just gave my GRE today after binging through your over the past couple of weeks. Was initially struggling with time management throughout my mocks, but managed to get a 326 (163/163) today! Wanted to thank you for all the tips and tricks. Your channel is gold and I’m going to recommend it to everyone I know who’s preparing for the GRE! Cheers :)
Incredible. Well done Yash!
One of the hardest topics on GRE Quant. Really happy you considered it for a video.
I wish you could arrange all your videos in a complete step by step course of quant and verbal. Please give it a consideration. Thanks!
I have! Check out my 5 week playlist
@@TheTestedTutor oh, I will check it. Thx Philips
You are the best ! The way you explain even the most complex concept in a such a simple way no one else can 😊
Hey, Philip I want to get tutions from you is it possible plz do reply 🤞
Can you plz help me with tutions
Thank you so much for this amazing and smooth teaching, I’m so lucky that I’ve found this video.
oh my god, this video is too hard for me, I need to practice more on probability problems, very valuable tips.
Thank you so much! Taking my test on the 20th and your videos have been extremely helpful in my final push
Dear Philip, For the unexpected probability trick (48:01), shouldn't we take the orders into consideration, and do the calculations for another time when we first pick the sibling from the class of 25 and then 12? meaning: 3/25 multiplied by 1/12? and then sum it with your answer.
Because with the twins you NEED to pick a twin the first time (no twin = fail), and then you NEED to pick that twin's one sibling (which is why you don't multiply by all the twins in the second class). But with the bag you can EITHER pick up red first, then green OR green then red. It is a more flexible situation with more routes to success.
It's the same reason we don't count H H (two heads) as different from H H (the same in reverse order). If we need two heads (like a twin pair) then first option must be a head (H), no alternative, no repeat or reversal
hey mann youre a real g fam i have my GRE tmr imma ace it cuz of your help (hopefully!)
Done with my GRE but um still watching Philip cause I love his content. ❤️
very cool
Thankyou for making these videos. I’m taking my GRE in about 2 weeks and I’m binge watching all your videos. Great help!
how did it go?
This is the most comprehensive video i have come across. You have covered every aspect, and i'd like to especially appreciate the order of topics you have chosen. Most tutors and books tell you about the 'letter method', but then go onto solve questions which dont require it! I have always, always been confused in that area and i am so grateful to you for finally clearing that up for me! The part when you said 'it's kind of cruel'... you can't know how relatable that was for me XD XD XD.
This video is amazing! Probability was always my weakness, and this video cleared a lot of the concepts. Thanks a lot!
This is the best guy for GRE out there
Thank you. I agree
41:11 Why should it be one choice followed by another choice and not picking both gloves simultaneously? Which part of the question helps us come to this conclusion?
Out of a blue. Honestly you are amazing. Incredible! How did you know exactly where I fail? Are you such a wizard?😅 Actually I got insane when you mentioned where most of students got wrong. You're amazing bro. I am totally thankful for you, whatever I say is less then you
A very nice video! Knowing combinatorics really helps with probability, but your video showed an alternative way for all these problems which now makes it easy for me to cross check!
I am studying for ISEE, and this video has helped me a lot.
This just makes so much sense when you explain it. Thank you so much for your help! I struggled with the probability questions on my practice exams and in the actual GRE, but you make to so simple.
Hi! As we know that Ets has increase the difficulty level of quant which is unjustified.
Sir, you are in a position where people will acknowledge you and support you. Please collaborate with other Gre tutors and specialists to record your protest at this injustice to ETS. Sir, please.
Thanks!
I have organised a march
@@TheTestedTutor
Hello Phillip!
I have asked Mr Saad to speak out against the unfair difficulty level of the Quant section, as well as the overall GRE exam. I mentioned that you are also protesting against this. Today he has a live session with Gmat club. He said he'd mention it in today's session, and he asked me that I should remind you also. You all can collaborate together and protest to ETS against this..
Thanks!
I have no words to thank you enough for this video..!!! 👍
Hi Philip
The 2nd last problem that you did 45:00 about twins, don't we have to do it like the way you did about the green and red beads 14:00
I too was thinking exactly the same 😂
exactly because they did not mention that the first choice has to be from the first class
Great video. You made learning probability easier. Thank you.
37:00 can also use complementary rule (1 - 0.4 = 0.6) then do 0.6 * 0.3 = 0.18.
Yeah, but 0.18 is not an answer choice and none of the given answers corresponds to it. In fractional form 0.18 would be 9/50, no?
@@reinhmr in other comments on this video, the uploader has confirmed that the corresponding answer choices he posted for that question aren’t the correct ones. 0.18 is still the correct answer. If you scroll down to older comments posted 8 months ago (at the time I’m writing this) you should find it. Such comments reference time stamps around the 37 or 38 minute mark.
@@gerardtyson2274 Thanks, Gerard. I should have read the whole thread before commenting. Great video, btw.
Hi Philip - Thank you so much for posting these videos. These are wayyyyy better than bulk of expensive materials available online.
Have a quick query on the question at 47th minute. The answer I am getting is 2%. The probablity of picking a twin could be (pick first from class 1 and then from class two) or (pick first from class 2 and then from class 1)
Sceanrio 1: 3/12 x 1/25
or
Sceanrio 2: 3/25x 1/12
= 1/100 + 1/100 = 2/100
Please correct me if i am wrong. and thanks again.
could it be because everytime questions mentions at random, I don't have to consider the order in which they are selected.
Hello Philip! I really can’t thank you enough for your videos; you’re helping accelerate my studying by light years! I just have a comment on this particular video about the ‘independent’ question; we computed the answer of 0.18 but it is none of the multiple choices given. Did we miss a step? Or was it the wrong set of answer choices?
Hi Philip same doubt here!
Awesome Mr. Philip..I have done magoosh twice but your videos are better and easy to understand...
But I have one question..In the sibling question, why we didn't consider another scenario that if I take one child from second class (25 student class), and then first class, the total calculation would be (3/12*1/25) 0 +3/25*1/12) . Please let me know...
Just saw this video of yours. Excellent content. Keep up the good work!
Thanks Saad
So helpful - thank you so much. Been binging your videos!
Hi Philip! Thank you for this amazing and very helpful video session.
Also, I had just one question in the 'Unexpected Probability Trick' at 48:00, Shouldn't we consider both the combinations Picking a Student from First class and then picking from larger class and vice-versa? In case that the probability would be twice of the current answer.
It’s what I thought so too. Because they didn’t specify the order of picking the students
Thank you... I was about to ask the same thing. Additionally, don't we have to consider the 'twin 1' OR 'twin 2' OR 'twin 3' when computing the first choice? In your first choice, you can either pick 'twin 1' or 'twin 2' or 'twin 3' in which case the probabilities need to be added.
Hi Philip, I had a doubt on the @44:48 question, Shouldn't there be two cases -
Case 1 - As you explained 3/12 X 1/25
+
Case 2 - 3/25 X 1/12
thank you so much for this video! the different kinds of problems were really helpful. love from india :)
Glad it helped!
Hi Philip! Thank you for the clear explanations and various questions example. I have some doubts regarding to question 11, 48:15 . Why do we not consider 3/25 × 1/12?
Hi Philip, thank you for providing great videos! I have a doubt at 38:15 in the independent probability section, the soluton is 0.18 but that doesn't match any of the options
Well spotted ctlr! My mistake, forgot to switch to decimal answer choices. Answer is indeed 0.18!
9/50 will be the answer, right?
@@dx5151 as a fraction, yes
@@dx5151 as a fraction, yes, i think the options were from the last question
A beginner Friendly video and also starts with question and explains the application along with it . Helpful to build concept at a grass root level which is very much important for Medium to hard level questions. so if somebody wants to start probability look this video first and then go else where
@The Tested Tutor, in case of disguised venn diagram, I have something to say. Actually the the probability of both event occurring is (0.4 * 0.5)=0.2=20%, Otherwise it doesn’t get matched with probability logic of two independent events. If they weren’t independent, then the word “both” wouldn’t come here.
Please tell me if I’m wrong here.
Hi Philip, can you kindly include a detailed lesson on standard deviation and statistics, including a set of challenging questions.
A great collection of questions:
Very nice video Philip! Thanks a lot!
Thank you for the wonderful video. Just a quick question: in the problem you explained in 47:06, Unexpected Probability Trick, how do we know we should start with smaller class and then find the twin in the larger class? Shouldn't we consider the probability of picking the first student from the larger class and its twin from the smaller class and then add these two probabilities? Thanks in advance.
I'm really really waiting for this topic. Actually I make this comment befor watch this, but after saw the thumbnail I got self confidence that ok, don't worry about probability. I will nailed it on exam. Wise me luck dude. I'm going to appear on my gre within 10 days..! And thanks for all and everything 💟. Luv from India.#
Best of luck Sathish!
how was your result, am going to take it soon ?
Probability: 31:00, 33:00 (Independent Prob), 39:00, 50:00
Thank you, this was very helpful!
Thank you phillip
Your videos are amazing. Keep it up.
38:18. Are the options wrong? I don't see any that correspond to the answer 18 percent..should we mark the answer closest to the answer figure?
Hello Phillip, thank you so much for the videos, I’m especially grateful for how to break down difficult concepts 😊. Regarding the first question on calculating opposites (@25:28) why can’t we just multiply 1/4 in four places, instead of calculating opposite and back to subtract from 1? Thank you
if u multiple 1/4 in all 4 places that would mean that it is raining on all four days.
47:31 In this qn shouldn't we also consider the fact that the order of selecting children frm 2 diff classes varies. So should we also calculate in both the possible ways as we did in red bead and green bead qn in which we were asked to find the possibility of 2 beads of diff colours is been picked?
Very good Philip!
Hiii Phillip
I just want to say THANK YOUUU🤗 for all these videos.
I took the GRE today and it didn’t go as planned, looking to take it again. What advice can you give me to be able to improve my score drastically
Looking forward to your reply
Thank youuu 🙏🏾❤️
You're welcome! Have you completed my 5 week playlist?
Thank you for replying. Yes I did. Excluded one or two videos because of time but I have watched 96% of all your videos.
@@Kut_Kut Have you managed to take and review all 5 ETS tests?
48:08 why aren't these independent selections? Why do they have to occur one after the other? Which part of the question gives us this idea? If the selections occur simultaneously, then the answer is 3%. i.e (3/12 * 3/25)
Great Work Philip!!! Appreciate your work to give us such a useful tricks.
Hey Philip! In the three twins question, why didn't we add the OR case where we can start with picking the first twin from larger class and second twin from smaller, giving us the probability as 1/100 + 1/100 = 2%?
Thanks sir 😊
Hey Philip, doesn't the provided solution for the last twin problem only consider the case where the child is selected from the smaller class first?
Do we not also have to consider the case where the child is selected from the larger class first?
i.e. P(both kids selected are sibling twins) = (3/12 * 1/25) + (3/25 * 1/12) = 6/300 = 2%?
I know this isn't one of the options but I guess I don't quite understand why...
pls teach table method for venn diagram in which there is maximizing minimizing too
At 48:10 shouldn't we consider two different cases of either the first twin was taken from class with 12 students and also the case where first twin was taken from a class of 25 students? Why did we only consider one case?
I was thinking the same thing, which is why i thought the answer was 2%... help Phillip! @TheTestedTutor
Hey Philip, For the question on 24:50, if I happen to choose the longer method of listing all the scenarios using letters and finding the probabilty, is there a way to determine that there are 15 such events. like how can I know that 15 events of snow and no snow is possible?
I have a doubt at 38:16, what is the correct answer? The concluded 0.18 does not match with any of the options, what am I missing?
He has corrected itin another comment.
WORTH WATCHING
So helpful!
Please how will you know whether you need to work out what you're not asked for and subtract from 1 or to work it out straight away?
At 48:15, shouldn't the answer be 2%? Because you found the probability of getting a kid in the smaller class and then matching them to one in the bigger class. But, you could also find a kid in the bigger class and then match them to one in the smaller class. Kind of like the GR RG example you talked about. So, shouldn't it be 1% times 2 or 2%?
Phillip, Thank you for your fantastic content!
Currently, I am on the week 5 Quant at your playlist. Suddenly, the playlist changed, and I found the probability part on week four, which was in the week 5 playlist.
Don't you think probabilities belong to the week 5 playlist?
I am lamenting!
Yes will sort that don't worry. It is because this video now has everything on probability.
@@TheTestedTutor Yes!! Great video Indeed. We appreciate your hard work, Brother!
Hello Phillip. Excellent video! Although, I am a bit confused about the twins question. Why weren't the ways of picking the siblings considered like in the case of the red and green marbles, please?
Because with the twins you NEED to pick a twin the first time (no twin = fail), and then you NEED to pick that twin's one sibling (which is why you don't multiply by all the twins in the second class). But with the bag you can EITHER pick up red first, then green OR green then red. It is a more flexible situation with more routes to success.
It's the same reason we don't count H H (two heads) as different from H H (the same in reverse order). If we need two heads (like a twin pair) then first option must be a head (H), no alternative, no repeat or reversal.
@@TheTestedTutor Thank you very much. And uh.. wish me good luck!! Thank you.
Hello Philip! Thank you so much for those videos; they’re nothing short of GOLD! In regards to this video, the Independent question of events P and Q. We concluded the answer 0.18 or 18% as the answer, but it is not one of the answer choices. Is there an additional final step? Or was it merely the wrong set of answer choices?
I was wondering the same thing as well.
Hey Philip! Just one query at 21:00 "one of many question", why is 9C3/9C4 wrong solution?
21:32 I am really confused. why didn't we find Philip x Christina + Christina and Philip like we did with the red and green balls when we found redx green + green x red? What is the difference? Please help
Hey Philip! Thanks always for the great content regarding GRE, personally I've never been more confident in quants after watching your in-depth videos. Just a question, do you have a dedicated quantitative content specifically to square roots (and/or cube roots)? If you haven't yet, I would be grateful if you can create about it soon! (cheers!!!)
Thanks teach!!
At 37.44, you give the answer that the probability of P not Q as 0.18. But the answer choices are in fractions, not decimals and none of the answer choices represents 0.18, which is fractional form would be 9/50, no?
Hello Phillip, So what is the answer at 38:12 Phillip? The explanation there is not clear.
Hello Philip,
In 19:23 what's the importance of "the next two interviews"?
If it is the next 3 interviews would the answer be the same?
Hey Phillip, in one of many - if Phillip and Christina are picked, wouldn't we consider both orders P C and C P? How do we know we don't need the orders?
Doing the orders will work and get the same answer but there are so many, like CPNN, PCNN, etc that it is simpler to do the shortcut of just multiplying as shown.
@@TheTestedTutor thanks! Is there a specific trick to identify one of many questions ?
Hi Philip! These are absolutely great videos, and have taught me so much! One request - could you make cloze videos? The type of cloze where you have to fill in the missing letters of words in a text? I know it usually doesn't come up in the GRE or GMAT, but it came up in my 11+ exam. Are there any techniques for being faster, or have a more efficient mindset for coming up with possible words? Thanks!
Ps. (Not trying to be rude) If you don't have much information on cloze or can't find out what sort of questions it has - since it doesn't appear in GRE or GMAT -
could you make distance videos? thanks once again
Hi Philip. For the independent question, why did we not just multiply probability of P occurring 0.3 with probability of Q not occurring 0.6?
Hi philip I am planning to take my gre in 2023 so I want to know if I will do all videos of your channel can I able to crack my gre with out any coaching??
What if we have 3 beads will this concept will be applicable on them too?
Hey Philip! Why aren'y we considering the order in the second unexpected probability trick question? like what if 1st child is selected from the larger class, it is not specified
Hi philip, for the question at 38:17 on independent, can't one just get the answer fairly quickly by using the probability of p happening which is 3/10 times q not happening witch is 6/10, and that would be 18/100?
But that's just p only happening. What about q only?
@@TheTestedTutor Thanks for the reply philip! I actually took the GRE today, your math tutorials have helped me get 166 in quant in the first try. You are awesome!
@@raining3110 amazing! Well done
for 3rd questons( 3P2+5p2)/8p2
love from nepal
this is beautiful
Hey philip! I have a query regarding last question. On computing total we have already divided by 2! to avoid redundancy due to double S then why is it necessary to take 2 choices for the want?
Hey Samikshya, an amazing spot, very well done. 2/120 works or 1/60 (depending on if we adjusted for the 2!) but not 1/30. I have edited the video to simplify. Do check out my Letter Arrangement video for further practice.
hey philip, i have a question.... what if on the GRE exam it does not specify whether or not the beads are not thrown back into the bag.... do we just automatically assume they are not? Thanks so much!! :)