Question:
The probability that A speaks truth is $\frac{4}{5}$ , while the probability for B is $\frac{3}{4}$. The probability that they contradict each other when asked to speak on a fact is
The probability that A speaks truth is $\frac{4}{5}$ , while the probability for B is $\frac{3}{4}$. The probability that they contradict each other when asked to speak on a fact is
Updated On: Jul 7, 2022
- $\frac{4}{5} $
- $\frac{1}{5} $
- $\frac{7}{20} $
- $\frac{3}{20} $
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The Correct Option is C
Solution and Explanation
A and B will contradict each other if one speaks truth and other false.
So, the required
Probability $ = \frac{4}{5} \left(1- \frac{3}{4}\right) + \left(1- \frac{4}{5}\right) \frac{3}{4} $
$ = \frac{4}{5} \times\frac{1}{4}+ \frac{ 1}{5} \times\frac{3}{4} = \frac{7}{20} $
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Notes on Multiplication Theorem on Probability
Concepts Used:
Multiplication Theorem on Probability
In accordance with the multiplication rule of probability, the probability of happening of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A happens given that event B occurs.
Let's assume, If A and B are dependent events, then the probability of both events occurring at the same time is given by:
\(P(A\cap B) = P(B).P(A|B)\)
Let's assume, If A and B are two independent events in an experiment, then the probability of both events occurring at the same time is given by:
\(P(A \cap B) = P(A).P(B)\)
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