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Probability

Section: Mathematics

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Question : 89 of 92

Marks: +1, -0

A student writes an examination which contains eight true or false questions. If he answers six or more questions correctly, he passes the examination. If the student answers all the questions, then the probability that he fails in the examination is

[AP EAPCET 18 May 2024 Shift 1]

$\;\; \frac{37}{256}$
$\;\; \frac{19}{256}$
$\;\; \frac{119}{256}$
$\;\; \frac{219}{256}$

Solution:

Here,

x=8, P=\;\frac{1}{2}

and

q=\;\frac{1}{2}

frobabllity that he will pass

\; =F X=\theta+P(X=7)+P(X=8

\; ={}^8 C_4 \left(\;\frac{1}{2}\right)^6 \left(\;\frac{1}{2}\right)^2+{}^8 C_7 \left(\;\frac{1}{2}\right)^3 \left(\;\frac{1}{2}\right)+{}^8 C_3 \left(\;\frac{1}{2}\right)^2

\; = \left(\;\frac{1}{2}\right)^2 P^3 C_2+{}^3 C_1+{}^8 C_4 1=\;\frac{37}{256}

Probability that he will fail is the cxamination

=1-\;\frac{37}{256}=\;\frac{219}{256}

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