Question

you draw one card from a 52 - card deck. then the card is replaced in the deck and the deck is shuffled, and you draw again. find the probability of drawing an ace the first time and a diamond the second time. click the icon to view a description of a standard deck of playing cards. the probability of drawing an ace the first time and a diamond the second time is (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate the probability of drawing an ace

There are 4 aces in a 52 - card deck. The probability of drawing an ace, \(P(A)\), is \(\frac{4}{52}=\frac{1}{13}\).

Step2: Calculate the probability of drawing a diamond

There are 13 diamonds in a 52 - card deck. The probability of drawing a diamond, \(P(D)\), is \(\frac{13}{52}=\frac{1}{4}\).

Step3: Use the multiplication rule for independent events

Since the card is replaced, the two draws are independent events. The probability of both events occurring is \(P(A)\times P(D)\).

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Answer:

\(\frac{1}{52}\)