Student A can solve 50% of problems, so P(A solves) = 21
Student B can solve 25% of problems, so P(B solves) = 41
Student C can solve 20% of problems, so P(C solves) = 51
To find the probability that at least one of them solves the problem, use the complement approach:
P(at least one solves) = 1 − P(none solve)
The probability that each student fails to solve the problem:
P(A fails) = 1−21
=21
P(B fails) = 1−41
=43
P(C fails) = 1−51
=54
Since the students work independently:
P(all fail) = P(A fails) × P(B fails) × P(C fails)
=21×43×54
=4012
=103
P(at least one solves) = 1−P(all fail)
=1−103
=107
Therefore, the probability that at least one of them will solve the problem is 107.