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

(a)
`(1)/(17)` (b)
`(1)/(16)`

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}}`

`=(13)/(52)`

`=(1)/(4)`

As sampling is done without replacement.

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

`=(12)/(51)`

`=(4)/(17)`

Probability that first card is club and second card is club
`=P(A)* P(B)`

`=(1)/(4)*(4)/(17)=(1)/(17)`

(b)

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

`=(13)/(52)`

`=(1)/(4)`

As sampling is done with replacement.

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

`=(13)/(52)`

`=(1)/(4)`

Probability that first card is club and second card is club
`=P(A)* P(B)`

`=(1)/(4)*(1)/(4)=(1)/(16)`