A pair of six-sided dice are rolled. Find the probability that the first die was 4 given that the sum of the dice was 9.

Question

 A pair of six-sided dice are rolled. Find the probability that the first die was 4 given that the sum of the dice was 9.

Answer 1

Hi Audrey, we need to solve the following:

 

P(A|B) = P(A∩B)/P(B), where

 

P(A|B) is the probability of A happening given B happened.

 

P(A∩B) is the probability of A and B occurring.

 

P(B) is the probability of B occurring.

 

Note, rolling two fair dice results in 36 possible pairs of numbers.

 

Here P(B) is the probability of the two dice summing to 9. There are four ways to roll 9 with a pair of fair dice, (3, 6), (4, 5), (5,4), and (6, 3).

 

P(B) = 4/36

 

P(A∩B) is the probability of a 4 on the first die and 5 on the second die. There is only one way for this to occur, (4, 5).

 

P(A∩B) = 1/36

 

P(A|B) = P(A∩B)/P(B) = (4/36) / (1/36) = 1/4

 

Questions?