The probability of event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then the probability of neither A and B occurring is

The probability of event $A$ occurring is $0.5$ and $B$ occurring is $0.3$ . If $A$ and $B$ are mutually exclusive events, then the
probability of neither $A$ and $B$ occurring is

A
0.6
B
0.5
C
0.7
D
0.2

Solution:

We have,

$P (A) = 0.5, P (B) = 0.3$

Required probability = $P (A \cap B) = P (A \cup B)$

$= 1 - P (A \cup B)$

$= 1 - {P (A) + P (B)}$ $[\begin{array}{l} ∵ A, B are mutually \\ exclusive events \end{array}]$

$= 1 - (0.5 + 0.3) = 0.2$

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