Question

# The events X and Y are mutually exclusive. suppose P(X) = 0.18 and P(Y) = 0.16...

The events X and Y are mutually exclusive. suppose P(X) = 0.18 and P(Y) = 0.16

What is the probability of either occurring?

What is the probability that neither will happen?

Solution:

Given,

The events X and Y are mutually exclusive i.e. P (X and Y) = 0

P(X) = 0.18

P(Y) = 0.16

1. Probability of either occurring.

P (Either X or Y) = P(X) + P(Y) - P (X and Y)

P (Either X or Y) = 0.18 + 0.16 - 0

P (Either X or Y) = 0.34

Hence, 0.34 is the probability of either occurring.

2. Probability of neither occurring.

P (Neither X nor Y) = 1 - P (Either X or Y)

P (Neither X nor Y) = 1 - 0.34

P (Neither X nor Y) = 0.66

Hence, 0.66 is the probability of neither occurring.

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