Suppose a and b are independent events. if p(a) = 0.4 and p(b) = 0.1, what is p(a u b)

Solution:

If a and b are two events of an experiment then the general rule of addition of probabilities of the two events is given as :

p(a ∪ b) = p(a) + p(b) - p(a and b) --- (1)

Where p(a) is the marginal probability of event a

p(b) is the marginal probability of event b

p(a and b) is the joint probability of events a and b

p(a) = 0.4

p(b) = 0.1

Since a and b are independent events their joint probability is given by the expression:

p(a and b) = p(a).p(b) = 0.4 × 0.1 = 0.04

Therefore,

p(a ∪ b) = 0.4 + 0.1 - 0.04

= 0.5 - 0.04

= 0.46

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Suppose a and b are independent events. if p(a) = 0.4 and p(b) = 0.1, what is p(a u b)

Summary:

If a and b are independent events. if p(a) = 0.4 and p(b) = 0.1 then p(a u b) 0.46