Question

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?

Answer 1

The probability of getting a diamond, replacing the card, then getting a red jack is `1/104`.

Explanation:

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

probability of getting a diamond is `13/52=1/4`

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

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

Hence, probability of getting a red jack is `2/52=1/26`

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

`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 `1/104`.