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

Answers ( )

    0
    2021-09-02T14:23:44+00:00

    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:

    [tex]P(Red)=\dfrac{18+x}{40+x}[/tex]

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

    [tex]\dfrac{18+x}{40+x}=0.5[/tex]

    [tex]18+x=0.5(40+x)[/tex]

    [tex]18+x=20+0.5x[/tex]

    [tex]x-0.5x=20-18[/tex]

    [tex]0.5x=2[/tex]

    Divide both sides by 0.5.

    [tex]x=\dfrac{2}{0.5}[/tex]

    [tex]x=4[/tex]

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

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

    [tex]40+4=44[/tex]

    Probability of getting a yellow cube is:

    [tex]P(Yellow)=\dfrac{\text{Number of yellow cubes}}{\text{Total number of cubes}}[/tex]

    [tex]P(Yellow)=\dfrac{9}{44}[/tex]

    Therefore, the required probability is [tex]P(Yellow)=\dfrac{9}{44}[/tex].

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