Question

A box contains 3 red, 4 black, and 7 green balls. If three balls are drawn one after the other at random with replacement, find the probability that all 3 are red.

Answer 1

To answer this question we will use the following expression to compute the probability that an event occurs:

`(FavorableOutcomes)/(TotalOutcomes).`

Since the choice is with replacement, then the probability of choosing a red ball is always the same.

The probability of choosing a red ball is:

`(3)/(3+4+7)=(3)/(14).`

Then the probability of choosing 3 red balls is:

`(3)/(14)*(3)/(14)*(3)/(14)=(27)/(2744).`

Answer:

`(27)/(2744).`