Question

In the bin there is a 45% chance of randomly selecting ripe avocados. If you are picking avocados from the bin, you keep inspecting avocados and stop upon finding a ripe avocado. If you buy a bag of avocados, you do not inspect the fruit until you get home and inspect the bag of avocados all at once.

1. What is the probability that you have inclusively between 2 and 3 ripe avocados from your bag of 5 avocados?
2. What is the probability that you inspect inclusively 3 and 3 avocados from the bin?

Answer 1

0.6125

Explanation:

We have,

P(ripe avocados) = 0.45 , n = 5

by binomial distribution,

P(x=k) =
`${\overset{n}C}_k P^k(1-P)^(n-k)$`

P(2 ≤ x ≤ 3) = P(x=2) + P(x=3)

P(x=2) =
`${\overset{5}C}_2(0.45)^2(0.55)^3$`

= 10 x (0.45)² x (0.55)³

= 0.3369

P(x=3) =
`${\overset{5}C}_3(0.45)^3(0.55)^2$`

= 10 x (0.45)³ x (0.55)²

= 0.2756

So, P(2 ≤ x ≤ 3 ) = 0.3369 + 0.2756

= 0.6125