The probability that A speaks truth is 45, while this probability for B is 34.The probability that they contradict each other when asked to speak on a fact is

A
$\frac{4}{5}$
B
$\frac{1}{5}$
C
$\frac{7}{20}$
D
$\frac{3}{20}$

Solution:

Consider the following events:

$E = A$ Speaks Truth, $, F = B$ Speaks Truth

We have $P (E) = \frac{4}{5}$ and $P (F) = \frac{3}{4}$

Required probability = $\begin{array}{l} = P ((E \cap \bar{F}) \cup (\bar{E} \cap F)) \\ = P (E \cap \bar{F}) + P (\bar{E} \cap F) \\ = P (E) P (F) + P (\bar{E}) P (F) \\ = \frac{4}{5} \times (1 - \frac{3}{4}) + (1 - \frac{4}{5}) \times \frac{3}{4} = \frac{7}{20} \end{array}$

The probability that A speaks truth is $\frac{4}{5}$ , while this probability for B is $\frac{3}{4}$ .The probability that they contradict each other when asked to speak on a fact is

Solution:

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