A lot of laptop computers contain 20 good ones and 3 defective ones. If two are selected and tested, find the probability that at least one will be defective.

Question

asked Mar 23, 2021 184k views

1 Answer

Kanga · Answer 1 · 2021-03-27T03:37:07+0000

Answer:
(63)/(253)

Explanation:

Given : Number of good laptops =20

Number of defective ones=3

Total laptops =23

If 2 laptops were selected, then the probability that none of them was defective would be =
(^(20)C_2)/(^(23)C_2)

$=((20!)/(2!18!))/((23!)/(2!21!))=(19*20)/(23*22)\\\\=(190)/(253)$

The probability that at least one will be defective= 1- P(none of them is defective)

=1-(190)/(253)=(63)/(253)

Hence, the probability that at least one will be defective.
=(63)/(253)