Question

Katy chose a card at random from a deck of 52 cards. Katy replaced the first card and then chose a second card. What is the probability that Katy chose a diamond both times?
A). 1/16
B). 1/52
C). 1/169
D). 1/208

Answer 1

52 total cards....13 total diamonds in the deck

P(1st card picked being a diamond) = 13/52
replacing the card, so the sample space remains the same
P(2nd card being a diamond) = 13/52

P(both) = 13/52 * 13/52 = 169/2704 = 1/16 <==

Answer 2

Any suit is a quarter of the deck, or 13 cards out of 52, so with replacement the probability of picking two straight of any suit is the same.

P(DD)=(1/4)(1/4)

P(DD)=1/16