Question

Suppose that two cards are randomly selected from a standard​ 52-card deck. ​(a) what is the probability that the first card is a spadespade and the second card is a spadespade if the sampling is done without​ replacement? ​(b) what is the probability that the first card is a spadespade and the second card is a spadespade if the sampling is done with​ replacement?

Answer 1

(a) without replacement:
P(S)=13/52=1/4
P(SS)=(1/4)*(12/51)=1/17
Probability of selecting two spades without replacement is 1/17.

(b) with replacement
P(S)=13/52=1/4
P(SS)=(1/4)(13/52)=1/16
Probability of selecting two spades with replacement is 1/16.