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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}
Using the addition law of probability, find 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
By the addition law of probability, we have
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
= 0.25 + 0.32 − 0.17
= 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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