Question

Two cards are selected from a standard deck of 52 playing cards. the first is replaced before the second card is selected. find the probability of selecting a diamond and then selecting a jack.

Answer 1

Sample space = 52
Jacks = 4
Diamonds = 13
P(D) = 13/52 = 1/4
P(J) = 4/52 = 1/13
.
P(D and J) = P(D) x P(J)
P(D and J) = 1/4 x 1/13
P(D and J) = 1/52
:)

Answer 2

Total cards = 52
Total diamonds = 13
Total Jacks = 4

P(a dimond and then a jack) = 13/52 x 4 /52 = 1/52

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Answer: The probability is 1/52.
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