Excellent question! We actually can't count identical rolls as interchangeable. The idea is that 2,6 and 6,2 actually represent two different things that can happen: 2 on the first roll & 6 on the second, or 6 on the first roll & 2 on the second. This means there are two possible first rolls that would get us to our result; the results are equivalent, but not identical. If we roll a 2 (which has a 1/6 chance), we can get to 8 by rolling 6 next (1/6 chance of that, so 1/36 chance of 2,6). If we roll a 6 (an additional 1/6 chance), we can get to 8 by rolling 2 next (making an extra 1/36 chance of getting 8 with 2 and 6). By contrast, there's only one way to get 4,4. We have to roll 4 both times. There's only one initial roll (4) that would work and only one follow-up that will get us what we want, so our chance of 4,4 is half that of 6,2/2,6. Hope that helps clarify!
In the last question, there is a much simpler method for the same. Probability that the first person is a part of a couple * Probability of the first winner's partner winning 1 *1/19 = 1/19
Watch the phrasing on that second question. We're looking at the chance of AT LEAST ONE 3. That could be one 3 or two 3's. So the second probability (11/36) is inclusive of the first (1/36). If we add 11/36 and 25/36, we do get 1, since we will always get either NO 3 or AT LEAST ONE 3.
What is the chance that each roll is at least 3? for this question while using the total - opposite method I am getting 8/9 as the ans
Can you please upload a video for standard deviation? Will be very helpful.
@53:43 why is the answer not 6/36?
Can't you roll a 4, 4 two ways? For example: 6, 2 can also be rolled 2, 6. Why can't 4, 4 be treated the same way?
Excellent question! We actually can't count identical rolls as interchangeable. The idea is that 2,6 and 6,2 actually represent two different things that can happen: 2 on the first roll & 6 on the second, or 6 on the first roll & 2 on the second. This means there are two possible first rolls that would get us to our result; the results are equivalent, but not identical. If we roll a 2 (which has a 1/6 chance), we can get to 8 by rolling 6 next (1/6 chance of that, so 1/36 chance of 2,6). If we roll a 6 (an additional 1/6 chance), we can get to 8 by rolling 2 next (making an extra 1/36 chance of getting 8 with 2 and 6). By contrast, there's only one way to get 4,4. We have to roll 4 both times. There's only one initial roll (4) that would work and only one follow-up that will get us what we want, so our chance of 4,4 is half that of 6,2/2,6. Hope that helps clarify!
@@manhattanprepgre7390 Thanks!
In the last question, there is a much simpler method for the same.
Probability that the first person is a part of a couple * Probability of the first winner's partner winning
1 *1/19 = 1/19
Hi Jessica. Exactly! That's the approach Dmitry recommends at 1:06:20!
could you please add standard deviation basic concept and also do solve some problems!!!!!!!!!!!!!!!!
Thanks for the feedback! I'll pass it along to our Instructor team.
at 43.51, sum of probability of getting both times 3 + neither times 3 + one time 3 is not equal to 1. i think probability of one time 3 is 10/36.
Watch the phrasing on that second question. We're looking at the chance of AT LEAST ONE 3. That could be one 3 or two 3's. So the second probability (11/36) is inclusive of the first (1/36). If we add 11/36 and 25/36, we do get 1, since we will always get either NO 3 or AT LEAST ONE 3.
This is pure gold!!
Yay! So happy you enjoyed it.
Not a good teacher. Very confusing!
Superb! You guys are doing an amazing job. Keep it up!!