Question

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.

Answer 1

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)`