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Q.

A student is given 6 questions in an examination with true or false type of answers. If he writes 4 or more correct answers, he passes in the examination. The probability that he passes in the examination is

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a

$\frac{7}{32}$

b

$\frac{5}{32}$

c

$\frac{3}{32}$

d

$\frac{11}{32}$

answer is C.

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Detailed Solution

n = 6
p = Probability of a question marked with correct answer
$= \frac{1}{2} \Rightarrow q = \frac{1}{2}$
$\begin{array}{l} P (X \geq 4) =^{6} C_{4} {(\frac{1}{2})}^{6} + \\ ^{6} C_{5} {(\frac{1}{2})}^{6} +^{6} C_{6} {(\frac{1}{2})}^{6} = \frac{1}{64} (15 + 6 + 1) \\ = \frac{22}{64} = \frac{11}{32} \end{array}$

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