Probability of happening an event A is 0.5 and that of B is 0.3 . If A and B are mutually exclusive

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14.Probability

easy

The probability of happening an event $A$ is $0.5$ and that of $B$ is $0.3$. If $A$ and $B$ are mutually exclusive events, then the probability of happening neither $A$ nor $B$ is

A

$0.6$

B

$0.2$

C

$0.21$

D

None of these

(IIT-1980)

Solution

(b) $P(\overline A \cap \overline B ) = P(\overline {A \cup B} ) = 1 – P(A \cup B)$

Since $A$ and $B$ are mutually exclusive, so

$P(A \cup B) = P(A) + P(B)$

Hence required probability $ = 1 – (0.5 + 0.3) = 0.2$.

Standard 11

Mathematics

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