Two groups, A and B wrote an exam. The probability of A's pass is 2/7 and the probability of B's pass is 2/5. What is the probability that only one of them is passed out?

Let, A be the event of the group A pass
Let, B be the event of the group B pass

Then,
A'= Event of the group A's fail and B'= event of the group B's fail.
Therefore, p(A) = 2/7 and p(B) = 2/5,
P(A') = 1 - P(A) = 1- 2/7 = 5/7 and P(B') = 1- P(B) = 1- 2/5 = 3/5

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) x P(B') + P(A') x P(B)
= (2/7 x 3/5) + (2/5 x 5/7)
= (6/35 + 10/35)
= 16/35