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Shubham draws a ball from a ball that contains white and yellow balls. The probability of choosing a white ball is $\frac{2}{9}$ . If the total number of balls in the bag is 36 then find the number of yellow balls.

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Detailed Solution

It is given that,
Total number of balls in the bag = 36,
Probability of selecting a white ball =

\frac{2}{9}

…. (1)
Find the number of yellow balls:
Let, number of yellow balls =

x

,
Then, number of white balls =

(36 - x)

Number of favorable outcomes =

(36 - x)

Total number of outcomes = 36
Since,

P = Number of trials in which the event E has happened Total number of trials

Then, probability of choosing a white ball

= 36 − x 36

Then from equation (1),

36 − x 36 = 29

⇒ 36 − x × 9 = 2 × 36

⇒ 36 − x = 2 × 36 9

⇒ 36 − x = 2 × 4

⇒ 36 − x = 8

⇒ x = 36 − 8

\Rightarrow

x = 28

Therefore, the number of yellow balls is 28.
Hence, option (1) is correct.

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