A bag contains 'x' red balls '2x' white balls and '3x

Discussion Forum : Probability I

Question -

A bag contains 'x' red balls '2x' white balls and '3x' black balls. 3 balls are drawn at random. The probability that all the balls drawn are of different colors is 0.3 .How many white balls are present in the bag?

Options:

A . 2

B . 4

C . 5

D . 7

Answer: Option A
:
A

P(All different)= $(^{x} C_{1}) \times (^{2 x} C_{1}) \times (^{3 x} C_{1}) / (^{6 x} C_{3})$

P(E)= $(6 x^{3}) \times \frac{6}{6 x} \times [(6 x - 1) \times (6 x - 2)] = \frac{3}{10}$

or, $\frac{3 x^{2}}{[(6 x - 1) \times (6 x - 2)]} = \frac{3}{10}$

$10 x^{2} = 18 x^{2} - 9 x + 1$

or, (x-1)(8x-1)=0

x can not be a fraction hence x=1

Total number of white balls= 2x=2

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