A problem in mathematics is given to 3 students. The probability of solving are 1/2, 1/3, 1/4. What is the probability that (i) the problem is solved, (ii) exactly one of them solved the problems.

Question

mathmate · Answer

To interpret in probability terms, this is a three step experiment (even though they are executed simultaneously, you can assume they are done 3 nanoseconds apart).
The probability of success of each experiment is 1/2, 1/3, 1/4, or p1,p2,p3.

(i) probability that  the problem is solved means that at least one of the students solved the problem.  This is the same as the complement of "no student solved the problem", which is easier to calculate.

(ii) probability that  exactly one of them solved the problems means that exactly one student solved the problem.  You could add together the probabilities of each of the three cases.

anonymous · Answer

if you type in the actual working of the problem..that would be great