Question

A basket contains six apples and five peaches. Three times, you randomly select a piece of fruit, return it to the basket, and then mix the fruit. All three times, the fruit is an apple. Find the probability of this occuring.

Answer 1

P( it occurring once) = 6/11

Now as the 3 events are independent we multiply the probs:-

P( apple picked 3 times) = 6/11 * 6/11 * 6/11 = 216/1331 or about 16.2%

Answer 2

16.22%

Explanation:

A basket contains six apples and five peaches.

Total fruits in the basket = 6 + 5 = 11

The probability of selecting a piece of fruit is an apple
`P_(1)=(6)/(11)`

Now return it to the basket and select a fruit. so all events are independent.

Therefore, the probability of each time selecting an apple is same.

Probability=
`P_(1)* P_(2)* P_(3)`

P =
`(6)/(11)`×
`(6)/(11)`×
`(6)/(11)`

=
`(216)/(1331)` = 16.22%

The probability of all three times the fruit is an apple is 16.22%