Question #232044

In a game, a card is taken at random from a full pack of 52 playing cards. It is then replaced, and a second card is taken. What is the probability that both cards are diamonds? O 0.225 O 0.625 O 0.0625 O 0.5 O 0.125

Expert's answer

Given information-

We have given a deck of 52 playing cards.

We know that we have 13 diamonds cards in a deck of 52 playing cards.

One by one we have to draw a card with a replacement.

We have to find the probability that both cards are diamonds.

Let A be the event that selecting diamonds cards.

**P(Selecting a diamond card at first draw) **= P(A) = **13/52**

Since we replace a card so the pack still remains 52 cards and, then we take a second card from the pack.

**P(Selecting a diamond card at second draw)** = P(B) = **13/52**

So the probability that drawing a diamond card for both the first and second draw is (13/52)*(13/52)

**P(Drawing both cards are diamonds)** = P(A)*P(B)= (13/52)*(13/52) = 1/16= **0.0625**.

**P(Drawing both cards are diamonds)** = **0.0625.**

Option **C** is the correct answer.

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