Question

Wooden boxes are commonly used for the packaging and transportation of mangoes. A convenience store regularly buys mangoes from a wholesale dealer. For every shipment, the manager randomly inspects five mangoes from a box containing 20 mangoes for damages due to transportation. Suppose the chosen box contains exactly 2 damaged mangoes.

a. Find the probability that the first mango is not damaged.
b. Find the probability that neither of the mangoes is damaged.
c. Find the probability that both mangoes are damaged.

Answer 1

Explanation:

Given that a convenience store regularly buys mangoes from a wholesale dealer. For every shipment, the manager randomly inspects five mangoes from a box containing 20 mangoes for damages due to transportation. Suppose the chosen box contains exactly 2 damaged mangoes.

In the selected box 18 good mangoes and 2 damaged mangoes are there

a) Find the probability that the first mango is not damaged.

= prob of selecting 1 from any one of 18 good mangoes =
`(18)/(20) =0.90`

b. Find the probability that neither of the mangoes is damaged. =

Prob of selecting 2 from 18 good mangoes

=
`(18C2)/(20C2) =0.5276`

c. Find the probability that both mangoes are damaged.

= Prob of selecting 2 from 2 bad mangoes

=
`(2C2)/(20C2) =0.005263`