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Q.

A student appeared in an examination consisting of 8 true-false questions. The student guesses the answers with equal probability. The smallest value of n, so that the probability at least 'n' correct answers in less than 1/2, is

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a

6

b

3

c

4

d

5

answer is D.

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Detailed Solution

$\begin{aligned} \Rightarrow \sum_{r = n}^{8}^{8} C_{r} {(\frac{1}{2})}^{8 - r} {(\frac{1}{2})}^{r} < \frac{1}{2} \\ \Rightarrow \sum_{r = n}^{8} C_{r} {(\frac{1}{2})}^{8} < \frac{1}{2} \\ \Rightarrow^{8} C_{n} +^{8} C_{n + 1} + \dots . +^{8} C_{8} < 128 \\ \Rightarrow 256 - (^{8} C_{0} +^{8} C_{1} + \dots . +^{8} C_{n - 1}) < 128 \\ \Rightarrow^{8} C_{0} +^{8} C_{1} + \dots . +^{8} C_{n - 1} > 128 \end{aligned}$

$n - 1 \geq 4 \Rightarrow n \geq 5$

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