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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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Verified Answer
The correct answer is:
$\frac{11}{32}$
$P($ Correct $)=\frac{1}{2}, P($ Wrong $)=\frac{1}{2}$
Passing in examination $\Rightarrow 4$ correct or 5 correct or 6 correct
$\begin{aligned} & ={ }^6 C_4\left(\frac{1}{2}\right)^4\left(\frac{1}{2}\right)^2+{ }^6 C_5\left(\frac{1}{2}\right)^5\left(\frac{1}{2}\right)^1+{ }^6 C_6\left(\frac{1}{2}\right)^6 \\ & =\left(\frac{1}{2}\right)^6\left[{ }^6 C_4+{ }^6 C_5+{ }^6 C_6\right] \\ & =\frac{1}{64} \cdot(15+6+1)=\frac{11}{32} .\end{aligned}$
Passing in examination $\Rightarrow 4$ correct or 5 correct or 6 correct
$\begin{aligned} & ={ }^6 C_4\left(\frac{1}{2}\right)^4\left(\frac{1}{2}\right)^2+{ }^6 C_5\left(\frac{1}{2}\right)^5\left(\frac{1}{2}\right)^1+{ }^6 C_6\left(\frac{1}{2}\right)^6 \\ & =\left(\frac{1}{2}\right)^6\left[{ }^6 C_4+{ }^6 C_5+{ }^6 C_6\right] \\ & =\frac{1}{64} \cdot(15+6+1)=\frac{11}{32} .\end{aligned}$
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