Question

A basket contains 8 pieces of fruit: 3 apples, 3 oranges, and 2 bananas. Jonas takes a piece of fruit at random from the basket, and then Beth takes a piece at random. What is the probability that Jonas will get an orange and Beth will get an apple?

Answer 1

The probability that Jonas will get an orange and Beth will get an apple is `9/56`.

Explanation:

This is the problem relating to conditional probability. This can be derived using multiplication rue, which states that `P[AnnB]=P[A]*P[B|A]`, i.e. probabillity of happening of both the events `A` and `B` is equal to probability of event `A` happening multiplied by probability of happening of event `B`, given `A` event has already happened.

As the basket contains `8` pieces of fruits of which `3` are oranges,

the probability that Jonas will get an orange is `3/8`.

Considering Jonas has already got an orange, as `7` fruits are left of which `3` are apple, probability that Beth will get an apple will be `3/7`.

Hence the probability that Jonas will get an orange and Beth will get an apple is `3/8xx3/7=9/56`.