Question

A bag contains white, black and red balls only. A ball is drawn at random from the bag. If the probability of getting a white ball is `3/10` and that of a black bail is `2/5`. find the total number of balls if number of red balls is `15.` Select the correct answer from above options

Answer 1

Let E be the event of getting a red ball. Then, P(getting a white ball) + P(getting a black ball) + P(E ) = 1 ` rArr 3/10+2/5 + P(E ) = 1 rArr 7/10 + P(E ) = 1` ` rArr P(E ) = 1 -7/10 = 3/10` ` rArr ` P(getting a red ball ) = `3/10`. Since P(getting a white ball) = P (getting a red ball), so the number of white balls is equal to the number of red balls, say x. `:. ` P(geting a red ball) = `x/(x+20+x) = x/(2x+20)`. ` :. x/(2x+20) = 3/10 rArr 10x = 6x + 60 rArr 4x = 60 rArr x = 15`. Hence, the total number of balls in the bag ` = 2x + 20 = 2 xx 15 + 20 = 50`.