First slide

Theorems of probability

Question

The probability that A speaks truth is_{$\frac{4}{5}$} , while this probability for B is_{$\frac{3}{4}$} . The probability that they contradict

Moderate

A

_{$\frac{4}{5}$}
B

_{$\frac{1}{5}$}
C

_{$\frac{7}{20}$}
D

_{$\frac{3}{20}$}

Solution

A and B will contradict each other if one speaks truth and other false
p(A)=4/5. p(B)=¾
=p(A) p( $B$ )+ $P (A)$ P(B)
So, the required probability $= \frac{4}{5} (1 - \frac{3}{4}) + (1 - \frac{4}{5}) \frac{3}{4}$
$= \frac{4}{5} \times \frac{1}{4} + \frac{1}{5} \times \frac{3}{4} = \frac{7}{20}$

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