Two cards are chosen at random from a deck of 52 cards. What is the probability of getting a diamond, replacing the card, then getting a red jack?

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Answer 1 · 2016-12-18T07:34:25

The probability of getting a diamond, replacing the card, then getting a red jack is $\frac{1}{104}$ $1/104$ .

As there are $13$ $13$ diamond cards in a deck of $52$ $52$ cards,

probability of getting a diamond is $\frac{13}{52} = \frac{1}{4}$ $13/52=1/4$

As we replace the card, the deck is as it is and

in deck of $52$ $52$ cards there are $2$ $2$ red jacks - one of diamond and another of hearts

Hence, probability of getting a red jack is $\frac{2}{52} = \frac{1}{26}$ $2/52=1/26$

As the two events are independent (due to replacement of card)

$P (A \cup B) = P (A) \times P (B) = \frac{1}{4} \times \frac{1}{26} = \frac{1}{104}$ $P(AuuB)=P(A)xxP(B)=1/4xx1/26=1/104$

Hence, the probability of getting a diamond, replacing the card, then getting a red jack is $\frac{1}{104}$ $1/104$ .