SOLUTION: Suppose a standard die is rolled twice. Let A be the event a 3 occurs on the first roll, let B be the event that the sum of the two rolls is 7, and let C be the event that the same

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Question 470613: Suppose a standard die is rolled twice. Let A be the event a 3 occurs on the first roll, let B be the event that the sum of the two rolls is 7, and let C be the event that the same number is rolled both times.
Find P(A), P(B), P(A~B) and determine if events A and B are independent.

Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 
Hi,
Event A, 3 on the 1st roll P(A) = 6/36 = 1/6
Event B, sum is 7 P(B) = 6/36 = 1/6
Event C, double P(C) = 6/36 = 1/6
If events are independent, then the probability of them both occurring is the
product of the probabilities of each occurring.
P(A and B)= P(A)*P(B) = 1/6*1/6 = 1/36 = P(both occur) a 3 rolled and then a 4
Events A and B are Independent
___1_2_3__4__5__6 (First roll)
1|_2_3_4__5__6__7
2|_3_4_5__6__7__8
3|_4_5_6__7__8__9
4|_5_6___8__9_10
5|_6_7_8__9_10_11
6|_7_8_9_10_11_12

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