Question

Suppose we randomly select 5 cards without replacement from an ordinary deck of playing cards. What is the probability of getting exactly 2 red cards (fi.e, hearts or diamonds)? Select one: O C O a. 0.22640 b, 0.32513 e. 0.29235 d.0.44259 e.0.19277

Answer 1

Hypergeometric Formula.. Suppose a population consists of N items, k of which are successes. And a random sample drawn from that population consists of n items, x of which are successes. Then the hypergeometric probability is:

h(x; N, n, k) = [ kCx ] [ N-kCn-x ] / [ NCn ]

This is a hypergeometric experiment in which we know the following:

• N = 52; since there are 52 cards in a deck.
• k = 26; since there are 26 red cards in a deck.
• n = 5; since we randomly select 5 cards from the deck.
• x = 2; since 2 of the cards we select are red.

We plug these values into the hypergeometric formula as follows:

h(x; N, n, k) = [ kCx ] [ N-kCn-x ] / [ NCn ]

h(2; 52, 5, 26) = [ 26C2 ] [ 26C3 ] / [ 52C5 ]

h(2; 52, 5, 26) = [ 325 ] [ 2600 ] / [ 2,598,960 ]

h(2; 52, 5, 26) = 0.32513

Thus, the probability of randomly selecting 2 red cards is 0.32513.