Question

A box contains 24 identical balls of which 12 are white and 12 are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the 4th time on the 7th draw is -

• A. 5/64
• B. 27/32
• C. 5/32
• D. 1/2

Answer 1

Answer: (C)

5/32

Answer 2

In any trail P(getting white ball) = 1/2

P(getting black ball) = ½ Required even will occur if in first six trial, 3 white balls are draw in any of the 3 trials from six. The remaining three trial must be kept reserved for black balls. This can happen

⁶C₃ × ³C₃ = 20 ways.

required probability = P(WWWBBB any permutation)W

20 × $\left( \frac { 1 } { 2 } \right) ^ { 3 }$ × $\left( \frac { 1 } { 2 } \right) ^ { 3 }$ × $\frac { 1 } { 2 }$ = 5/32