Final answer:
To find the probability that the math problem will be solved by at least one of the students, calculate the probability that none solve it and subtract from 1. The answer is 11/15, assuming independent attempts by each student.
Step-by-step explanation:
The question is about calculating the probability that a math problem will be solved by at least one of the three students, given their individual chances of solving it. To find this probability, we can use the concept of complementary probability - basically, we calculate the probability that none of the students solve the problem and subtract this from 1.
Let's call the event that A solves the problem 'A', B solves it 'B', and C solves it 'C'. The probability that A does not solve it is 1 - 1/3 = 2/3, that B does not solve it is 1 - 1/5 = 4/5, and that C does not solve it is 1 - 1/2 = 1/2. Assuming the events are independent, the probability that none of them solve the problem is:
(2/3) × (4/5) × (1/2) = 8/30 = 4/15
Therefore, the probability that the problem is solved by at least one student is:
1 - 4/15 = 11/15
This result is based on the assumption that the students' attempts are independent events and neither's performance affects the others.