Suppose that a family has four children consisting of two gi

Suppose that a family has four children, consisting of two girls and two boys. Call the girls Abigail and Brianna; call the boys Charles and Duane. Suppose further that two of these children are to be selected at random.

1. List the sample space of all possible pairs of these four children.

2. Determine the probability that one child of each gender will be selected.

3. Determine the expected value of the number of girls who will be selected.

4. Write a sentence or two interpreting what this expected value means in this context.

5. If both boys are selected, would it be reasonable for the girls to cry foul and claim that the selection process must not have been random? Explain your answer, and refer to a relevant probability calculation.

Solution

2 girls, 2 boys

1) Sample space= (Abigail, Brianna) ( (Abigail, Charles)(Abigail, Duane) (Brianna, Duane) (Brianna,Charles) (Charles,Duane)

2) n(one gender to be selected) = 1+1+1+1 =4

3)No of girls can be 0, 1 ,2

prob 1/6 4/6 1/6

Expected value of girls = 0+4/6+2/6 = 1

4) Expected value is the average no of girls normally expected in the selection

5) If both boys are selected prob = 1/6 and cannot be called as random.

Hence girls crying is right.