Exercise 22 Page 968

If the occurrence of an event does not affect the occurrence of another event, then those events are called independent events. If $A$ and $B$ are independent events, then the following rule applies for the probability of this type of compound event. Recall that the probability of an event is the ratio of favorable outcomes to possible outcomes. In this exercise, we draw from the standard deck of cards. Out of $52$ cards in the deck, there are $4$ cards numbered three. Now, we know enough to calculate a probability of drawing a card number $3$ from the stack. We are told that the first card drawn is returned to the stack before drawing the next card. This means that these events are independent and the number of possible outcomes for the second card remains $52.$ Since we want the second card to be a queen, the number of favorable outcomes is $4.$ With this information we can calculate $P(\text{Queen}).$ Finally, we can find the value of drawing, in order, a three and a queen. The probability of subsequently drawing a three and a queen from the deck is equal to $\frac{1}{169}.$