First slide

Theorems of probability

Question

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

Moderate

A

0.2
B

0.8
C

0
D

0.3

Solution

$P (A) = 0.5, P (B) = 0.3, A \cap B = ϕ$
$P (A \cup B) = P (A) + P (B)$

$= 0.5 + 0.3 = 0.8$

$P (\bar{A} \cap \bar{B}) = 1 - 0.8 = 0.2$

$∴$ The probability of neither A nor B occurring is 0.2

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