Question
Download Solution PDFFind the probability of occurrence of at least one of A and B, If A and B are two independent events?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A and B are two independent events.
Concept:
For any two independent events A and B : P(A ∩ B) = P(A)·P(B)
Explanation:
The probability of occurrence of at least one of A and B means " A but not B or B but not A or A and B both ".
Indirectly it means '1 - probability of occurrence of neither A and B'.
⇒ P(at least one of A and B) = 1 - P(neither A and B)
⇒ P(at least one of A and B) = 1 - P(A' ∩ B')
Now, P(A' ∩ B') = P(A’) P(B’) as A and B are independent events.
⇒ P(at least one of A and B) = 1 - P(A')P(B')
Last updated on May 26, 2025
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