# There are 3 red and 8 green balls in a bag. If you randomly choose balls one at a time, with replacement, what is the probability of choosing 2 red balls and then 1 green ball?

##### 2 Answers

#### Explanation:

The fact that the ball is replaced each time, means that the probabilities stay the same each time a ball is chosen.

P(red, red, green) = P(red) x P(red) x P(green)

=

=

Reqd. Prob.

#### Explanation:

Let **Red Ball** is chosen in the **First Trial**

**Red Ball** is chosen in the **Second Trial**

**Green Ball** is chosen in the **Third Trial**

:. Reqd. Prob.

For

There are **3 Red** + **8 Green** = **11** balls in the bag, out of which, **1** ball can be chosen in **11** ways. This is total no. of outcomes.

Out of **3 Red** balls, **1 Red** ball can be chosen in **3** ways. This is no. of outcomes favourable to

For

This is the Conditional Prob. of occurrence of

, knowing that **the Red ball chosen in R_1** has to be **replaced back** in the bag **before a Red ball for R_2** is to be chosen. In other words, this means that the situation remains same as it was at the time of

Finally, on the same line of arguments, we have,

From

Reqd. Prob.

Hope, this will be helpful! Enjoy Maths.!