Question

A shipment of 40 fancy calculators contains 3 defective units. What is the probability if a college bookstore buys 20 calculators out of this shipment and 1 is defective.

Answer 1

38.46%

Explanation:

There are no names or marking that can make the calculator look different, so the order is not important. Then we should use a combination to solve this problem.

There are 40 calculators in one shipment, 37 of them good items and 3 of them are defect items. We need to choose 19 good calculators and 1 defect calculator. The number of ways to do that will be:

`(37)/(19)`*
`(3)/(1)`= 37!
`(37!)/(19!(37-19!)) * (3!)/(1!(3-1)!)`= 53017895700

The number of possible ways to choose 20 calculators out of 40 calculators will be:

`(40)/(20)`=
`(40!)/(20!(40-20!))`=137846528820

The chance will be: 53017895700/ 137846528820 = 0.3846= 38.46%