Question

A grocery store manager took inventory of all the fruit to decide what needed to be donated. Of the 8 pieces of fruit deemed "overripe," 6 were peaches.

If the manager randomly selected 5 of the overripe pieces for the first donation package, what is the probability that all of them are peaches?

Answer 1

The probability of randomly selecting 5 peaches from 8 pieces of overripe fruit, where 6 are peaches, is 0.0714 or 7.14%.

Step-by-step explanation:

The question refers to the calculation of the probability that all five randomly selected pieces of overripe fruit are peaches.

There are a total of 8 pieces of fruit, of which 6 are peaches and 2 are not.

To find the probability, we calculate the probability of choosing peaches 5 times in a row without replacement from the 6 peaches available out of the 8 total pieces of fruit.

This is a combination problem and can be calculated as:

1. Probability of first peach = 6/8
2. Probability of second peach = 5/7 (after one peach has been removed)
3. Probability of third peach = 4/6
4. Probability of fourth peach = 3/5
5. Probability of fifth peach = 2/4

Multiplying these probabilities gives us the overall probability of selecting 5 peaches in a row:

Probability of all five being peaches = (6/8) * (5/7) * (4/6) * (3/5) * (2/4)

= 0.0714 or 7.14%