## Aysha has 40 cubes in a bag. 18 red cubes. 13 blue cubes. 9 yellow cubes. Aysha adds some more red cubes into the ba

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.

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1 year 2021-09-02T14:21:59+00:00 1 Answers 0 views 0

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