Question

Suppose a packing box contains 24 smartphones, of which two phones are defective. If, while setting up a store display, a salesclerk selects 10 smartphones at random from the box without replacement, what is the probability that both defective smartphones will be selected and put on display?

Answer 1

Let X is a random variable shows the number of defective out of 10. Here X has hypergeometric distribution with following parameters :

Population size: N = 24

Sample size: n= 10

Number of defectives in sample: k = 2

The probability that both defective smartphones will be selected and put on display is

$P(X=2)=\frac{\binom{2}{2}\binom{24-2}{10-2}}{\binom{24}{10}}=0.1630$