A problem is given to three students whose chances of solving it are 1/5, 1/4 and 1/3 respectively. What is the probability that the problem will be solved?

Question: A problem is given to three students whose chances of solving it are 1/5, 1/4 and 1/3 respectively. What is the probability that the problem will be solved?

Solution:
Probability of 1st student solving the problem = 1/5
Probability of 1st student not solving the problem = 1 - (1/5) = 4/5
Probability of 2nd student solving the problem = 1/4
Probability of 2nd student not solving the problem = 1 - (1/4) = 3/4
Probability of 3rd student solving the problem = 1/3
Probability of 3rd student not solving the problem = 1 - (1/3) = 2/3
Probability that none of the students solve the problem = (4/5) × (3/4) × (2/3)
= 2/5

∴ Probability that the problem will be solved = 1 - (2/5)
= 3/5