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

Answer 1

Answer:

a) $\frac{1}{221}$

b) $\frac{1}{169}$

Step-by-step explanation:

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

We know, In set of 52 -cards deck two sets of 26 are back and red and further into four of 13 sets spade,club,diamond,heart with numbers (2,3,4,5,6,7,8,9,10,J,Q,K,Q,A)

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

Number of kings = 4

Probability of getting first card is a king $\frac{4}{52}$

The second card is a king if the sampling is done without​ replacement

Probability of getting second card is a king $\frac{3}{51}$

The probability that the first card is a king and the second card is a king if the sampling is done without​ replacement is given by,

$P=\frac{4}{52}\times \frac{3}{51}$

$P=\frac{12}{2652}$

$P=\frac{1}{221}$

​(b) What is the probability that the first card is a king and the second card is a king if the sampling is done with​ replacement?

Number of kings = 4

Probability of getting first card is a king $\frac{4}{52}$

The second card is a king if the sampling is done with​ replacement

Probability of getting second card is a king $\frac{4}{52}$

The probability that the first card is a king and the second card is a king if the sampling is done with​ replacement is given by,

$P=\frac{4}{52}\times \frac{4}{52}$

$P=\frac{16}{2704}$

$P=\frac{1}{169}$