Question
Download Solution PDFThe probability that at least one of the events A and B occur is 0.6. If A and B occur simultaneously with probability 0.2, then the value of P(Ac) + P(Bc) will be
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Some useful formulas are:
The probability of the complement of an event is one minus the probability of the event.
We can write, P (A’) or P (Ac) or
P(A ⋃ B) = P(A) + P(B) - P(A ⋂ B)
Calculation:
P(A) = 1 - P(Ac)
P(B) = 1 - P(Bc)
P(A ⋃ B) = P(A) + P(B) - P(A ⋂ B)
∴ P(A) + P(B) = P(A ⋃ B) + P(A ⋂ B)
∴ [1 - P(Ac)] + [ 1 - P(Bc)] = 0.2 + 0.6
∴ 2 - [P(Ac) + P(Bc)] = 0.8
∴ P(Ac) + P(Bc) = 2 - 0.8
∴ P(Ac) + P(Bc) = 1.2
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