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Question
A sample space consists of 9 elementary events E1, E2, E3, ..., 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 addting the probabilities of elementary events.
Solution
Let S be the sample space of the elementary events.
S = {E1, E2, E3, ..., E9}
Given:
A = {E1, E5, E8}
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 = {E1, E5, E8}
B = {E2, E5, E8, E9}
Now, 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
Notes
The solution of the problem is provided by taking P(E5) = 0.1. This information is missing in the question as given in the book.
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