Question

A big contains 4 white balls and some red balls. If the probability of drawing a white ball from the bag is `2/5`, find the number of red balls in the bag.

Answer 1

The number of white balls is 4. Let the number of red balls is x. Then the total number of trials is 4 + x .

Let A be the event of drawing a white ball.

The number of times A happens is 4.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by P (A) and is given by

` P (A) = m/n`

Therefore, we have `P(A) = 4/(4+x)`.

But, it is given that ` P (A) = 2/5` . So, we have

` 4/(4+x) =2/5`

⇒2(4 + x ) = 20

⇒ 8 + 2x = 320

⇒ 2x = 20-8

⇒2x = 12

⇒ x =`12/6`

⇒ x =6

Hence the number of red balls is 6 .