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:

$P(Red)=\dfrac{18+x}{40+x}$

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

$\dfrac{18+x}{40+x}=0.5$

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

$18+x=20+0.5x$

$x-0.5x=20-18$

$0.5x=2$

Divide both sides by 0.5.

$x=\dfrac{2}{0.5}$

$x=4$

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:

$P(Yellow)=\dfrac{\text{Number of yellow cubes}}{\text{Total number of cubes}}$

$P(Yellow)=\dfrac{9}{44}$

Therefore, the required probability is $P(Yellow)=\dfrac{9}{44}$.