For any two events, \(A, B\) if \(P(A \cup B)=a P(A \cap B)+b P(A)+c P(B)\), then \(3 a+2 b+5 c=\) ?
For any two events, \(A, B\) if \(P(A \cup B)=a P(A \cap B)+b P(A)+c P(B)\), then \(3 a+2 b+5 c=\) ?
2
4
3
1
Solution
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.