the probability of solving a question by ABC is 1/2, 1/3, 1/4 respectively find the probability 1) exactly one of them will solve the question 2) exactly two of them solve the question 3) question is not solved 4) at least one of them solve the question
Answers
Answer:
Probability of A solving the problem = P(A) = 1/2
Probability of B solving the problem = P(B) = 1/3
Probability of C solving the problem = P(C) = 1/6
Problem will be solved when i) either one of A, B, C solve the problem, ii) two of A, B, C solve the problem, OR iii) all of A, B, C solve the problem
Problem will not be solved when - all of A, B, C are not able to solve the problem
Probability of A not solving the problem = P(A) = 1/2
Probability of B not solving the problem = P(B) = 2/3
Probability of C not solving the problem = P(C) = 5/6
Probability of problem not being solved = A, B, C not solving the problem simultanously = P(A)*P(B)*P(C) = (1/2)*(2/3)*(5/6)
= 5/18
Probability of problem being solved = 1 - probability of problem not being solved
= 1 - (5/18) = 13/18