Study the following information carefully and answer the given questions.
There were some red, some green and some white balls in a bag. Probability of drawing 1 white ball from the bag is . `(1)/(3)` If there were 6 more red balls in the bag, the probability of getting 1 green ball would have been `(1)/(30)` less.
If Probability of drawing 1 green ball from the bag is `(1)/(5)` , then what is the probability of drawing 2 balls such that none of them is red?

Options

A. 20
B. 30
C. 24
D. 16

Answer

C

Explanation

Let the total number of balls in the bag = `(3 xx 5) x = 15 x ` then
Number of white balls ` = 15 x xx (1)/(3) = 5 x ` and sum of the number of white and red balls
` = 15 x xx (4)/(5) = 12 x` , then
Number of red balls ` = 12 x - 5 x = 7 x` and number of green balls = 15 x - 12 x = 3x
Also, ` (3 x)/( 15 x) - (3x)/( ( 15 x + 6)) = (1)/(30)`
`rArr ( 3x )/( ( 15 x + 6)) = (1)/(6)`
`rArr x = 2 `
So, number of red balls = 7x = 14 and number of white balls = 5x = 10
Hence, the required number of balls = 14 + 10 = 24.