A problem in mathematics is given to 4 students A, B, C, D. Their chances of solving the problem, respectively, are

What is the probability that

(i) The problem will be solved?

(ii) At most one of them will solve the problem?

Given Data:

• Probability that A solves the problem

• Probability that B solves the problem

• Probability that C solves the problem

• Probability that D solves the problem

Calculation:

Say P(E) is probability that problem is solved

Probability that problem is not solved by anyone of A, B, C and D

Therefore

Probability that problem is solved is

At most one of them solves the problem means that we have to consider two cases

• when no one solves the problem

• when either one of them solves the problem

Therefore desired probability