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
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.