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

Answer:

a.$\frac{1}{17}$

b.$\frac{1}{16}$

Step-by-step explanation:

We are given that two cards are drawn are randomly selected from a standard 52- cards deck.

Total cards=52

Total number of spade cards=13

Probability=$\frac{number\;of\;favourable\;cases}{total\;number\;of cases}$

a.The probability of drawing two cards first card is spade and second card is spade without replacement =$\frac{13}{52}\times \frac{12}{51}$

The probability of drawing two cards first card is spade and second card is spade=$\frac{1}{17}$

b. The probability of drawing two cards first is spade and second card is a spade with replacement =$\frac{13}{52}\times\frac{13}{52}$

The probability of drawing two cards first is spade and second card is a spade with replacement =$\frac{1}{16}$