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प्रश्न
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}
Using the addition law of probability, calculate P(A ∪ B)
उत्तर
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
P(A ∪ B) = P(A) + P(B) – P(A ∩ B) .....(i)
But P(B) = P(e2) + P(e5) + P(e8) + P(e9)
= 0.08 + 0.1 + 0.07 + 0.07
= 0.32
And P(A ∩ B) = {e5, e8}
= P(e5) + P(e8)
= 0.1 + 0.07
= 0.17
Putting the values in equation (i) we get
P(A ∪ B) = 0.25 + 0.32 – 0.17
= 0.40
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