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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

564

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B

2732

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C

532

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D

12

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Solution

The correct option is C

532


An explanation for the correct option:

Step 1: Find the probability for a white ball is drawn and find the probability for a black ball is drawn

We have been given that, 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.

We need to find the probability that a white ball is drawn for the 4th time on the 7th draw.

Since there is a box contains 24 identical balls, of which 12 are white and 12 are black.

Let, p:The probability that white ball is drawn

p=1224p=12

q:The probability that black ball is drawn

q=1224q=12

Step 2: Find the required probability.

The probability that a white ball is drawn for the 4th time on the 7th draw.

This means the white ball is drawn 3 times in the first 6 draws.

So, the required probability would be,

P=C36×(12)3×(12)3×(12)P=6!3!(6-3)!×(12)7P=20×1128P=532

Therefore, option (C) is the correct answer.


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