InterviewSolution
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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 randomly from the box, the probability that both balls are of green color is 1/15. Find the total number of balls in the box.1). 152). 203). 304). 45 |
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Answer» 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 = 6/15 Let G + B = 10x R + G = 6x 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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