That's a very good explanation! Many people also get the following question wrong, so please explain. [Question] Find the probabilities that the following events will occur when two dice are rolled. ①Both show odd numbers ②One shows odd number and another shows evenn number ③Both show even number P(E):the probability that event E occurs. 【Distinguishable dice A and B】 (the number that dice A shows,the number dice B shows):event If we only judge whether the numbers indicated by the dice are odd or even, the following four events will occur. (odd,odd) (odd,even) (even,odd) (even,even) If each event occurs with equal probability, the probability is 1/4. Therefore, P(①)=1/4, P(②)=1/2, P(③)=1/4 (1) If we judge the number(1,2,···,6) indicated by the dice ,the following 36 events will occur. (1,1), (1,3),(1,5) (1,2),(1,4),(1,6) (3,1), (3,3),(3,5) (3,2),(3,4),(3,6) (5,1), (5,3),(5,5) (5,2),(5,4),(5,6) (2,1), (2,3),(2,5) (2,2),(2,4),(2,6) (4,1), (4,3),(4,5) (4,2),(4,4),(4,6) (6,1), (6,3),(6,5) (6,2),(6,4),(6,6) If each event occurs with equal probability, the probability is 1/36. Therfore P(①)=9×(1/36)=1/4, P(②)=18×(1/36)=1/2, P(③)=9×(1/36)=1/4 (2) (2) matches (1). 【Indistinguishable two dice】 (odd,even)is the same event as(even,odd). Thererore, if we only judge whether the numbers indicated by the dice are odd or even, the following three events will occur. (odd,odd) (even,odd) (even,even) If each event occurs with equal probability, the probability is 1/3. Therefore P(①)=1/3, P(②)=1/3, P(③)=1/3 (3) (1,3) is the same event as (3,1). If we judge the number(1,2,···,6) indicated by the dice ,the following 21 events will occur. (1,1) (3,1), (3,3) (5,1), (5,3),(5,5) (2,1), (2,3),(2,5) (2,2) (4,1), (4,3),(4,5) (4,2),(4,4) (6,1), (6,3),(6,5) (6,2),(6,4),(6,6) If each event occurs with equal probability, the probability is 1/21. Therefore P(①)=6×(1/21)=2/7, P(②)=9×(1/21)=3/7, P(③)=6×(1/21)=2/7 (4) (4) contradicts (3).
Hello need help with this one -- Show logical notation that expresses following statement: If one dice shows an even number of spots and the second dice shows an odd number of spots, then the total for the pair is less than or equal to 9.
(E ∧ O) → T ≤ 9 Where: E = 'even' O = 'odd' T = 'total' L = 'less than or equal to' This notation can be read as: "If E is true and O is true, then T is less than or equal to 9." In other words, if the first dice shows an even number of spots and the second dice shows an odd number of spots, then the total number of spots on the two dice is less than or equal to 9.
A 10 sided die is tossed. What is the probability of getting: a. multiple of 3 b. divisors of 8 c. numbers less than 10 d. cube numbers e. square numbers
If you roll two dice the chances of you rolling a double is 1/6 rolling a chosen double (5 and 5 for example) is 1/36 ...I make the proposition that making a guess of a number between 1 and 6 is like rolling a dice in your head. So, if you throw a dice 1/6 And guess the number .....isn't the probability of you guessing correctly the same as throwing two dice? ...so shouldn't the chance of you guessing correctly be 1/36....? (Yet you and I both know that rolling a dice can only yield 6 possible outcomes) So is the probability 1/6 or 1/36....?
That's a very good explanation!
Many people also get the following question wrong, so please explain.
[Question]
Find the probabilities that the following events will occur when two dice are rolled.
①Both show odd numbers
②One shows odd number and another shows evenn number
③Both show even number
P(E):the probability that event E occurs.
【Distinguishable dice A and B】
(the number that dice A shows,the number dice B shows):event
If we only judge whether the numbers indicated by the dice are odd or even, the following four events will occur.
(odd,odd) (odd,even)
(even,odd) (even,even)
If each event occurs with equal probability, the probability is 1/4.
Therefore, P(①)=1/4, P(②)=1/2, P(③)=1/4 (1)
If we judge the number(1,2,···,6) indicated by the dice ,the following 36 events will occur.
(1,1), (1,3),(1,5) (1,2),(1,4),(1,6)
(3,1), (3,3),(3,5) (3,2),(3,4),(3,6)
(5,1), (5,3),(5,5) (5,2),(5,4),(5,6)
(2,1), (2,3),(2,5) (2,2),(2,4),(2,6)
(4,1), (4,3),(4,5) (4,2),(4,4),(4,6)
(6,1), (6,3),(6,5) (6,2),(6,4),(6,6)
If each event occurs with equal probability, the probability is 1/36.
Therfore
P(①)=9×(1/36)=1/4, P(②)=18×(1/36)=1/2, P(③)=9×(1/36)=1/4 (2)
(2) matches (1).
【Indistinguishable two dice】
(odd,even)is the same event as(even,odd).
Thererore, if we only judge whether the numbers indicated by the dice are odd or even, the following three events will occur.
(odd,odd)
(even,odd) (even,even)
If each event occurs with equal probability, the probability is 1/3.
Therefore
P(①)=1/3, P(②)=1/3, P(③)=1/3 (3)
(1,3) is the same event as (3,1).
If we judge the number(1,2,···,6) indicated by the dice ,the following 21 events will occur.
(1,1)
(3,1), (3,3)
(5,1), (5,3),(5,5)
(2,1), (2,3),(2,5) (2,2)
(4,1), (4,3),(4,5) (4,2),(4,4)
(6,1), (6,3),(6,5) (6,2),(6,4),(6,6)
If each event occurs with equal probability, the probability is 1/21.
Therefore
P(①)=6×(1/21)=2/7, P(②)=9×(1/21)=3/7, P(③)=6×(1/21)=2/7 (4)
(4) contradicts (3).
Best explenation ever, my math teacher never mentioned this stuff
Thanks
WHAT
Tricky but cool
I am your teacher, Actually you were not listening attentively that time, although I tried my best.😂😂Now don't mentioned me in comments ok.
Hello need help with this one --
Show logical notation that expresses following statement: If one dice shows an even number of spots and the second dice shows an odd number of spots, then the total for the pair is less than or equal to 9.
(E ∧ O) → T ≤ 9
Where:
E = 'even'
O = 'odd'
T = 'total'
L = 'less than or equal to'
This notation can be read as: "If E is true and O is true, then T is less than or equal to 9."
In other words, if the first dice shows an even number of spots and the second dice shows an odd number of spots, then the total number of spots on the two dice is less than or equal to 9.
Thanks I needed this before my exam
A 10 sided die is tossed. What is the probability of getting:
a. multiple of 3
b. divisors of 8
c. numbers less than 10
d. cube numbers
e. square numbers
A: 0.3, 30% chance
B: 0.4, 40% chance
C: Including 1 0.3 30% chance, otherwise 0.2 20% chance
D: 0.2 20% chance
E: also 0.2 20% chance
Hopefully I am correct.
Thanks
whats the difference between probability and odds? In my language it means both the same :(
When calculating odds you have wins over losses.
How do you know that though because odds are probabilities as well
I think you were meant to say “2 and 12.” Not 1. There is no chance of one haha
What if the question says rolling a special number?
2 4 6
K.I.S.S thats for everyone. This shit aint complicated
keep it stupid simple! :)
IF THREE dice are rolled then
216 possible combinations. 11 is the most common number
If you roll two dice the chances of you
rolling a double is 1/6
rolling a chosen double (5 and 5 for example) is 1/36
...I make the proposition that making a guess of a number between 1 and 6 is like rolling a dice in your head.
So, if you throw a dice 1/6
And guess the number .....isn't the probability of you guessing correctly the same as throwing two dice?
...so shouldn't the chance of you guessing correctly be 1/36....?
(Yet you and I both know that rolling a dice can only yield 6 possible outcomes)
So is the probability 1/6 or 1/36....?