Question:
If A and B are mutually exclusive events , given that $P(A) = \frac{3}{5} , P(B) = \frac{1}{5}$, then P(A or B) is
If A and B are mutually exclusive events , given that $P(A) = \frac{3}{5} , P(B) = \frac{1}{5}$, then P(A or B) is
Updated On: May 22, 2024
- 0.8
- 0.6
- 0.4
- 0.2
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The Correct Option is A
Solution and Explanation
Given $P(A) = \frac{3}{5}$ and $P(B) =\frac{1}{5}$
P(A or B) = P(A $\cup$ B) = P(A) + P(B) (because A and B are mutually exclusive)
$ = \frac{3}{5} + \frac{1}{5} = \frac{4}{5} = 0.8 $
P(A or B) = P(A $\cup$ B) = P(A) + P(B) (because A and B are mutually exclusive)
$ = \frac{3}{5} + \frac{1}{5} = \frac{4}{5} = 0.8 $
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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:
\(P(A \cap B) = P(A).P(B)\)
Read More: Multiplication Theorem on Probability