Probability Question 263
Question: If A and B are two independent events such that $ P(A\cap B’)=\frac{3}{25} $ and $ P(A’\cap B)=\frac{8}{25}, $ then $ P(A)= $
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Options:
A) $ \frac{1}{5} $
B) $ \frac{3}{8} $
C) $ \frac{2}{5} $
D) $ \frac{4}{5} $
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Answer:
Correct Answer: A
Solution:
Since events are independent. So, $ P(A\cap {B}’)=P(A)\times P({B}’)=\frac{3}{25} $
$ \Rightarrow P(A)\times {1-2P(B)}=\frac{3}{25} $ …..(i)
Similarly, $ P(B)\times {1-P(A)}=\frac{8}{25} $ …..(ii)
On solving (i) and (ii), we get $ P(A)=\frac{1}{5} $ and $ \frac{3}{5} $ .
BETA
