In a competition two persons, A and B wrote an exam. The probability of A's pass is 3/7 and the probability of B's pass is 3/5. What is the probability that only one of them is passed out?

Let A be the event of the person A pass

Let B be the event of the person B pass

Then, A' = Event of the person A's fail and

B' = Event of the person B's fail.

Therefore, P(A) = 3/7 and P(B) = 3/5,

P(A') = 1 - P(A) = 1 - 3/7 = 4/7 and P(B') = 1 - P(B) = 1 - 3/5 = 2/5

Required probability = P[(A and B') Or (B and A')]

= P[(A and B') or (B and A')]

= P[(A and B') + (B and A')]

= P[(A and B')] + P[(B and A')]

= P(A) × P(B') + P(A') × P(B)

\(= \left({\frac{3}{7} \times \frac{2}{5}} \right) + \left({\frac{3}{5} \times \frac{4}{7}} \right)\)

\(= \left({\frac{6}{{35}} + \frac{{12}}{{35}}} \right) = \frac{{18}}{{35}}\)