The problem involves three students attempting to solve independently with probabilities 21, 31, and 41 respectively.
To find the probability that at least one student solves the problem, calculate the probability that none of them solve it, then subtract from 1.
The probability each student fails:
Student 1 fails: 1−21=21
Student 2 fails: 1−31=32
Student 3 fails: 1−41=43
Since the students work independently, the probability all three fail:
P(all fail)=21×32×43
P(all fail)=246
P(all fail)=41
The probability at least one student solves the problem:
P(problem solved)=1−P(all fail)
P(problem solved)=1−41
P(problem solved)=43
Therefore, the probability that the problem is solved is 43.