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

This is a hypergeometric experiment where;

N = 52;52 cards in a deck.

k = 26; 26 red cards in a deck.

n = 5; 5 cards from the deck,

x = 2; 2 of the cards we select are red.

Now using hypergeometric formula :

h(x; N, n, k) = [ _kC_x ]* [ _N-kC_n-x ] / [ _NC_n ]

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.

So the correct option is (b)0.32513