AP EAMCET · Maths · Probability
For any two events, \(A, B\) if \(P(A \cup B)=a P(A \cap B)+b P(A)+c P(B)\), then \(3 a+2 b+5 c=\) ?
- A 2
- B 4
- C 3
- D 1
Answer & Solution
Correct Answer
(B) 4
Step-by-step Solution
Detailed explanation
As we know for any two events \(A\) and \(B\) \(P(A \cup B)=P(A)+P(B)-P(A \cap B)\) Now, on comparing with the given equation \(P(A \cup B)=a P(A \cap B)+b P(A)+c P(B)\) Then, we get \(a=-1, b=1, c=1\) \(\therefore \quad 3 a+2 b+5 c=3(-1)+2+5=4\) Hence, option (b) is correct.
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