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Q.

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 balls is drawn for the 4^th time on the 7^th drawn is

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a

$5 / 64$

b

$5 / 32$

c

$1 / 2$

d

$27 / 32$

answer is C.

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Detailed Solution

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Probability of a getting a white ball in a single draw

$= p (w) = \frac{12}{24} = \frac{1}{2} \Rightarrow p (B) = \frac{1}{2}$

Probability of getting a white ball 4^th time in the 7^th draw

=P(getting 3 W in 6 draws) x P(getting W ball at 7^th draw)

$= {}^{6}C_{3} {(\frac{1}{2})}^{3} \times {(\frac{1}{2})}^{3} \times \frac{1}{2} = \frac{5}{32}$

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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 balls is drawn for the 4th time on the 7th drawn is