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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}
Compute P(A), P(B) and P(A ∩ B).
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
P(A) = P(E1) + P(E5) + P(E8) = 0.08 + 0.1 + 0.07 = 0.25
P(B) = P(E2) + P(E5) + P(E8) + P(E9) = 0.08 + 0.1 + 0.07 + 0.07 = 0.32
Now, A ∩ B = {E5, E8}
∴ P(A ∩ B) = P(E5) + P(E8) = 0.1 + 0.07 = 0.17
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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