Question

two cards are selected from a standard deck of 52 playing cards. the first card is not replaced before the second card is selected. find the probability of selecting a nine and then selecting a five.
the probability of selecting a nine and then selecting a five is □
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the probability of selecting a nine first

There are 4 nines in a deck of 52 cards. So the probability of selecting a nine, \(P(\text{nine})\), is \(\frac{4}{52}=\frac{1}{13}\).

Step2: Calculate the probability of selecting a five after a nine is drawn

Since the first card (a nine) is not replaced, there are now 51 cards left in the deck. There are 4 fives. So the probability of selecting a five given that a nine was selected first, \(P(\text{five}|\text{nine})\), is \(\frac{4}{51}\).

Step3: Use the multiplication rule for dependent events

The multiplication rule for dependent events is \(P(A\cap B)=P(A)\times P(B|A)\). Here \(A\) is the event of selecting a nine and \(B\) is the event of selecting a five. So \(P(\text{nine and then five})=\frac{4}{52}\times\frac{4}{51}\).

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Answer:

\(0.006\)