The probability that the problem is not solved by any of the students is the product of the probabilities that each student fails to solve the problem. So we have:
P(problem not solved) = P(X fails) * P(Y fails) * P(Z fails)
P(X solves the problem) = 1/4 P(X fails to solve the problem) = 1 - P(X solves the problem) = 3/4 P(Y solves the problem) = 3/7 P(Y fails to solve the problem) = 1 - P(Y solves the problem) = 4/7 P(Z solves the problem) = 2/9 P(Z fails to solve the problem) = 1 - P(Z solves the problem) = 7/9
So we have:
P(problem not solved) = (3/4) * (4/7) * (7/9) = 1/3
Therefore, the probability that the problem could not be solved is 1/3. Answer: (a)