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

Algebra ->  Probability-and-statistics -> 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      Log On


   

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) About Me  (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_highlight%287%29__8__9_10

5|_6_7_8__9_10_11

6|_7_8_9_10_11_12