2. Suppose the probabilities of having a boy or a girl child are the sameboth are 50%. Answer the following questions about a couple that has two children, showing any calculations.

a. What is the probability that the couple has two girls?

b. The eldest of the two children is a girl. Given this, what is the probability that the couple has two girls?

1/2

c. At least one of the children is a girl. What is the probability that the couple has two girls?

2/3

Your answers to a, b, and c should all be different numbers. Explain why each is different from the others. (Hint: (b) specifies that the older child is a girl, while (c) simply states that one of the two children is a girl without indicating whether it's the older or younger child.)

3. Consider the following three sets of data

A = {4, 10, 11, 7, 15}

B = {10, 10, 10, 10, 10}

C= {1, 10, 19, 1, 22}

a. Without doing any calculations, explain which data set has the largest standard deviation.

b. For each data set, calculate the mean, median, and mode. (Remember to show your work!)

c. For each data set, calculate the range, variance, and standard deviation. (Remember to show your work!)