Question

Aysha has 40 cubes in a bag.

18 red cubes.
13 blue cubes.
9 yellow cubes.
Aysha adds some more red cubes into the bag.
Aysha is now going to take at random a cube from the bag
The probability now that she will take a red cube is 0.5.
Work out the probability that she will take a yellow cube.

Answer 1

Given:

Total number of cubes = 40

Red cubes = 18

Blue cubes = 13

Yellow cubes = 9

Aysha adds some more red cubes into the bag.

The probability now that she will take a red cube is 0.5.

To find:

The probability that she will take a yellow cube.

Solution:

Let Aysha adds x red cubes into the bag. Then,

Number of total cubes = 40+x

Number of red cubes = 18+x

Probability of getting a red cube is:

`P(Red)=(18+x)/(40+x)`

The probability now that she will take a red cube is 0.5. So,

`(18+x)/(40+x)=0.5`

`18+x=0.5(40+x)`

`18+x=20+0.5x`

`x-0.5x=20-18`

`0.5x=2`

Divide both sides by 0.5.

`x=(2)/(0.5)`

`x=4`

It means Aysha adds 4 more red cubes into the bag.

Now, the total number of cubes int he bag is:

`40+4=44`

Probability of getting a yellow cube is:

`P(Yellow)=\frac{\text{Number of yellow cubes}}{\text{Total number of cubes}}`

`P(Yellow)=(9)/(44)`

Therefore, the required probability is
`P(Yellow)=(9)/(44)`.