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Question
A sample space consists of 9 elementary outcomes e1, e2, ..., e9 whose probabilities are
P(e1) = P(e2) = 0.08, P(e3) = P(e4) = P(e5) = 0.1
P(e6) = P(e7) = 0.2, P(e8) = P(e9) = 0.07
Suppose A = {e1, e5, e8}, B = {e2, e5, e8, e9}
List the composition of the event A ∪ B, and calculate P(A ∪ B) by adding the probabilities of the elementary outcomes.
Solution
Given that: S = {e1, e2, e3, e4, e5, e6, e7, e8, e9}
A = {e1, e5, e8} and B = {e2, e5, e8, e9}
P(e1) = P(e2) = 0.08
P(e3) = P(e4) = P(e5) = 0.1
P(e6) = P(e7) = 0.2, P(e8) = P(e9) = 0.07
A ∪ B = {e1, e2, e5, e8, e9}
∴ P(A ∪ B) = P(e1) + P(e2) + P(e5) + P(e8) + P(e9)
= 0.08 + 0.08 + 0.1 + 0.07 + 0.07
= 0.40
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