Test Index

Probability Part 1

Section: Mathematics

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Question : 93 of 100

Marks: +1, -0

The probability that

A

speaks truth is

\frac{4}{5}

, while the probability for

B

\frac{3}{4}

. The probability that they contradict each other when asked to speak on a fact is

$\frac{4}{5}$
$\frac{1}{5}$
$\frac{7}{20}$
$\frac{3}{20}$

Solution:

The probability of speaking truth by

A, P(A)=\frac{4}{5}

. The probability of not speaking truth by

A, P(\overline{A})=1-\frac{4}{5}=\frac{1}{5}

.

The probability of speaking truth by

B, P(B)=\frac{3}{4}

. The probability of not speaking truth of

B, P(\overline{B})=\frac{1}{4}

.

The probability that they contradict each other

=P(A)\times P(\overline{B})+P(\overline{A})\times P(B)

=\frac{4}{5}\times\frac{1}{4}+\frac{1}{5}\times\frac{3}{4}

=\frac{1}{5}+\frac{3}{20}=\frac{7}{20}

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