Question

From a standard deck of 52 playing cards:

Draw 3 cards without replacement.

Find the probability that you get at least one red card.

(Due to rounding, select the best answer)

Group of answer choices

0.22

0.50

0.79

0.88

Answer 1

Solution:

N = 52

S = 26 (Number of red cards in total 52 cards)

3 cards are selected without replacement from 52 cards

n = 3 (Sample size)

Let X be the number of red card in the sample

Given the hypergeometric distribution with

N = 52 , S = 26, n = 3

The PMF of the hypergeometric distribution is

P(X = x) =     ; x = 0 , 1 2 .....,n

Now

P(at least 1 red card)

= P(X 1)

= 1 - { P(X < 1) }

= 1 - { P( X = 0) }

=

= 1 -  0.117647059

=  0.882352941

= 0.88

Answer : 0.88