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A box contains red, green and blue colored balls. When one ball is drawn randomly from the box, the probability that it is either green or blue is 2/3. Also, the probability that the ball drawn randomly from the box is either red or green is 3/5. When two balls are drawn one after another from the box, the probability that both balls are of green color is 1/15. Find the total number of balls in the box.

A box contains red, green and blue colored balls. When one ball is drawn randomly from the box, the probability that it is either green or blue is 2/3. Also, the probability that the ball drawn randomly from the box is either red or green is 3/5. When two balls are drawn one after another from the box, the probability that both balls are of green color is 1/15. Find the total number of balls in the box. Correct Answer 45

Let the number of red, green and blue balls be R, G and B respectively.

When one ball is drawn randomly from the box, the probability that it is either green or blue = 2/3 = 10/15

The probability that the ball drawn randomly from the box is either red or green = 3/5 = 9/15

Let G + B = 10x

R + G = 9x

R + G + B =15x

By solving above equations, we get

R = 5x

G = 4x

B = 6x

Probability of picking two green balls = (4x/15x) × ((4x – 1)/(15x – 1))

But, when 2 balls are drawn at random, the probability that they both are of green color = 1/15

⇒ (4x/15x) × ((4x – 1)/(15x – 1)) = 1/15

⇒ 4(4x – 1) = (15x – 1)

⇒ 16x – 4 = 15x – 1

⇒ 16x – 15x = 4 – 1

⇒ x = 3

∴ Total no. of balls in box is 45

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