Question

A bag contains 15 marbles. The probability of randomly selecting a green marble is One-fifth. The probability of randomly selecting a green marble, replacing it, and then randomly selecting a blue marble is 2 over 25 . How many blue marbles are in the bag?

Answer 1

Given:

Total number of marbles = 15

Probability of randomly selecting a green marble = $\dfrac{1}{5}$.

Probability of randomly selecting a green marble, replacing it, and then randomly selecting a blue marble = $\dfrac{2}{25}$.

To find:

The number of blue marbles.

Solution:

Let the number of blue marbles be x.

$\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$

$P(Blue)=\dfrac{x}{15}$

It is given that,

$P(Green)=\dfrac{1}{5}$

Probability of randomly selecting a green marble, replacing it, and then randomly selecting a blue marble is $\dfrac{2}{25}$. So,

$P(Green)\times P(Blue)=\dfrac{2}{25}$

$\dfrac{1}{5}\times \dfrac{x}{15}=\dfrac{2}{25}$

$\dfrac{x}{75}=\dfrac{2}{25}$

Multiply both sides by 75.

$\dfrac{x}{75}\times 75=\dfrac{2}{25}\times 75$

$x=2\times 3$

$x=6$

Therefore, the number of blue marbles in the bag is 6.