Question

A basket contains four apples and five peaches. Three times, you randomly select a piece of fruit, return it to the basket, and then mix the fruit. The first time, you get an apple. Then second and third times, you get peaches. Find the probability of this occuring.

Answer 1

It’s either 100/729 or approximately 13.72%

Answer 2

Probability is :
`(100)/(729)`

Explanation:

A basket contains four apples and five peaches.

Total number of fruits =
`4+5=9`

Probability of apple being selected = number of apples / total number of fruits =
`(4)/(9)`

Probability of peach being selected = number of peaches / total number of fruits =
`(5)/(9)`

As replacement is allowed, the probability of selecting an apple in the any attempt will remain
`(4)/(9)` and the probability of selecting a peach will remain
`(5)/(9)`

So, the required probability will be :

`(4)/(9)* (5)/(9)* (5)/(9)`

=
`(100)/(729)`