Question

In a bag which contains 50 balls, there are 25 red balls and some green and blue balls.
If two balls are picked up from the bag with replacement, then the probability of the
first ball being red and second being green is 3/20. Find the number of green balls in
the bag?

Answer 1

Given :

A bag contains 50 balls. 25 are red and some green and blue.

To Find :

The number of green balls in the bag.

Solution :

A bag contains the number of balls = 50

The number of red balls = 25

Two balls are picked up from the bag with replacement. Both events are independent.

The probability of the first ball being red (P₁) = $\frac{25}{50}=\frac{1}{2}$

The probability of the first ball being red and second being green is $\frac{3}{20}$.

Let the number of green balls be 'n'

The probability of picking second ball is green (P₂) = $\frac{n}{50}$

Probability = P₁ × P₂

$\frac{1}{2}\times \frac{n}{50}=\frac{3}{20}$

$\frac{n}{50}=\frac{3}{20}\times \frac{2}{1}$

$\frac{n}{50}=\frac{3}{10}$

$n=\frac{3\times 50}{10}$

$n=\frac{150}{10}$ = 15

There are 15 green balls in the bag.