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 clubclub and the second card is a clubclub if the sampling is done without​ replacement? ​(b) What is the probability that the first card is a clubclub and the second card is a clubclub if the sampling is done with​ replacement?

Answer 1

Answer:

(a)$\frac{1}{17}$ (b) $\frac{1}{16}$

Step-by-step explanation:

GIVEN: Suppose that two cards are randomly selected from a standard​ $52$ card deck.

TO FIND: (a) What is the probability that the first card is a club and the second card is a club if the sampling is done without​ replacement? ​(b) What is the probability that the first card is a club and the second card is a club if the sampling is done with​ replacement.

SOLUTION:

(a)

Probability that first card is club $P(A)=\frac{\text{total club cards}}{\text{total cards}}$

                                                   $=\frac{13}{52}$

                                                   $=\frac{1}{4}$

As sampling is done without replacement.

probability that second card is club  $P(B)=\frac{\text{total club cards}}{\text{total cards}}$

                                                            $=\frac{12}{51}$

                                                            $=\frac{4}{17}$

Probability that first card is club and second card is club $=P(A)\times P(B)$

                                                                                             $=\frac{1}{4}\times\frac{4}{17}=\frac{1}{17}$

(b)

Probability that first card is club $P(A)=\frac{\text{total club cards}}{\text{total cards}}$

                                                   $=\frac{13}{52}$

                                                   $=\frac{1}{4}$

As sampling is done with replacement.

probability that second card is club  $P(B)=\frac{\text{total club cards}}{\text{total cards}}$

                                                            $=\frac{13}{52}$

                                                            $=\frac{1}{4}$

Probability that first card is club and second card is club $=P(A)\times P(B)$

                                                                                             $=\frac{1}{4}\times\frac{1}{4}=\frac{1}{16}$