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.
`(1)/(17)`

b.
`(1)/(16)`

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=
`(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 =
`(13)/(52)* (12)/(51)`

The probability of drawing two cards first card is spade and second card is spade=
`(1)/(17)`

b. The probability of drawing two cards first is spade and second card is a spade with replacement =
`(13)/(52)*(13)/(52)`

The probability of drawing two cards first is spade and second card is a spade with replacement =
`(1)/(16)`