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

Answer:

38.46%

Step-by-step 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:

$\frac{37}{19}$* $\frac{3}{1}$= 37!$\frac{37!}{19!(37-19!)} * \frac{3!}{1!(3-1)!}$= 53017895700

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

$\frac{40}{20}$= $\frac{40!}{20!(40-20!)}$=137846528820

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