Question

What's the probability of the compound event for. A bag contains 4 red, 8 blue, 6 yellow and 2 green marbles. Maria selects a marble, puts it back and then selects a second marble. P (blue, red)

Answer 1

Given:

Number of red marbles = 4

Number of blue marbles = 8

Number of yellow marbles = 6

Number of green marbles = 2

To find:

The probability of getting a blue marble then a red marble, i.e., P(blue, red).

Solution:

Using the given information,

The total number of marbles = 4+8+6+2

                                                = 20

Probability of getting a blue marble in first draw is

$P(Blue)=\dfrac{\text{Number of blue marbles}}{\text{Total number of marbles}}$

$P(Blue)=\dfrac{8}{20}$

$P(Blue)=\dfrac{2}{5}$

Maria selects a marble, puts it back and then selects a second marble. It means the total number of marbles remains the same.

$P(red)=\dfrac{\text{Number of red marbles}}{\text{Total number of marbles}}$

$P(red)=\dfrac{4}{20}$

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

Now, the probability of getting a blue marble then a red marble is

$P(blue,red)=\dfrac{2}{5}\times \dfrac{1}{5}$

$P(blue,red)=\dfrac{2}{25}$

Therefore, the required probability P(blue, red) is $\dfrac{2}{25}$.