Given : A,B,C are mutually exclusive events and exhaustive events
P(B) = (3/2) P(A) and P(C) = (1/2) P(B)
To find : P(A)
Formula used : P(A) + P(B) + P(C) = 1
For mutually exclusive events A,B,and C , P(A and B) = P(B and C) = P(A and C)= 0
Let P(A) = x , P(B) = (3/2) P(A) = \(\frac{3}{2}x\) , P(C) = (1/2) P(B) = \(\frac{1}{2}\times\frac{3}{2}x\) = \(\frac{3}{4}x\) + \(\frac{3}{2}x\) + \(\frac{3}{4}x\) = 1
\(\frac{13}{4}x\) = 1
\(x=\frac{4}{13}\)
P(A) = x = \(\frac{4}{13}\)
P(A) = \(\frac{4}{13}\)
