1. Consider an ordinary deck of 52 playing cards, which has the usual sequence of 13 cards in each of four suits (hearts, diamonds, spades, and clubs). You draw a card at random from the deck. Answer the following questions. For each, explain your reasoning or show your calculation.

a. What is the probability that the card is the queen of diamonds?

b. What is the probability that the card is any queen?

c. What is the probability that the card is either a queen or a red ace?

d. What is the probability that the card is not a queen or a red ace?

e. Given that you have drawn a queen, what is the probability that the card is a

diamond?

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?

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

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!)