2.1.18 problem 20

(a)

Since the second card is equally likely to be any of the remaining $3$ cards, the probability that both cards are queens is $\frac{1}{3}$.

(b)

Our sample space now consists of all order pairs of the two queens and the two jacks, where at least one card is a queen. Since all the outcomes are equally likely, the answer is $\frac{2}{10}=\frac{1}{5}$.

(c)

Now, the sample space consists of all order pairs of the two queens and the two jacks, where one of the cards is the Queen of Hearts. Thus, the answer is $\frac{2}{6}=\frac{1}{3}$.