The probability that A speaks truth is 45, while this probability for B is 34.

Discussion Forum : Probability I

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 each other when asked to speak on a fact is

Options:

A .

\frac{3}{23}

B .

\frac{1}{20}

C .

\frac{1}{5}

D .

\frac{14}{40}

Answer: Option D
:
D

In short the event described here is P(A)'P(B) +P(A)P(B)'

where P(A) and P(B) are the probabilities of A and B speaking the truth respectively.

P(E)= P(A)'P(B) +P(A)P(B)' = $\frac{1}{5} \times \frac{3}{4} + \frac{4}{5} \times \frac{1}{4}$

P(E)= $\frac{3}{20} + \frac{4}{20} = \frac{7}{20} = \frac{14}{40}$

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