Question
Download Solution PDFIf A and B are mutually exclusive events with \(\rm P(A)=\frac{1}{2} P(B)\), then P(A) = ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A and B are mutually exclusive events with \(\rm P(A)=\frac{1}{2} P(B)\)
Concept:
If A and B are mutually exclusive events then
P(A ∩ B) = 0
Calculation:
A and B are mutually exclusive events then
P(A ∩ B) = 0
we know that
P( A ⋃ B) = P(A) + P(B) - P(A ∩ B)
⇒ P( A ⋃ B) = P(A) + P(B)
On substituting the values P(A ⋃ B) means total probability then
⇒ 1 = P(A) + 2P(A) (since \(\rm P(A)=\frac{1}{2} P(B)\))
⇒ 3P(A) = 1
⇒ \(\rm P(A)=\frac{1}{3}\)
Hence the option (1) is correct.
Last updated on Jun 19, 2025
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