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 five and then selecting an eight.
the probability of selecting a five and then selecting an eight is
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the probability of selecting a five first

There are 4 fives in a deck of 52 cards. So the probability of selecting a five, \(P(\text{five})\), is \(\frac{4}{52}\).

Step2: Calculate the probability of selecting an eight after a five

After one card (a five) is drawn and not replaced, there are 51 cards left. There are 4 eights in the deck. So the probability of selecting an eight given that a five has been drawn, \(P(\text{eight}|\text{five})\), 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 five and \(B\) is the event of selecting an eight. So \(P(\text{five and eight})=\frac{4}{52}\times\frac{4}{51}\).

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Answer:

\(0.006\)