Chapter 13.5, Problem 4CYP

To determine

Find the probability that one die is a 4 , given that the sum of the two die is 9.

Answer to Problem 4CYP

J

Explanation of Solution

Given:

Two dice are rolled.

Formula Used:

Conditional Probability

The conditional probability of B given A is :

  $P(B|A)=\frac{P(A\text{ and }B)}{P(A)};P(A)\ne 0$

Calculation:

Let A be the event that the sum of the two die is 9.

Let B be the event that one die is a 4.

We need to find the probability that one die is a 4 , given that the sum of the two die is 9.

The set of pairs of die whose sum is 9 = A = { (3,6) , (4,5) , (5,4) , (6,3) }

The set of pairs of die where one die is a 4 , from the set A = { (4,5) , (5,4)}

So, there are 4 pairs of die whose sum is 9 in the sample space , and only 2 out of these have a 4 on one die.

Therefore,

  $P(B|A)=\frac{P(A\text{ and }B)}{P(A)}=\frac{2}{4}=\frac{1}{2}$

So , the correct option is J.