# A problem in statistics is given to three students A, B, and C. Their chances of solving the problem are 13, 14, and 15 respectively. If all of them try independently, what is the probability that - Mathematics and Statistics

Sum

A problem in statistics is given to three students A, B, and C. Their chances of solving the problem are 1/3, 1/4, and 1/5 respectively. If all of them try independently, what is the probability that, problem is solved?

#### Solution

Let A be the event that student A can solve the problem.
B be the event that student B can solve problem.
C be the event that student C can solve problem.

∴ P(A) = 1/3, P(B) = 1/4 and P(C) = 1/5

P(A') = 1 − P(A) = 1-1/3=2/3

P(B') = 1 − P(B) = 1-1/4=3/4

P(C') = 1 − P(C) = 1-1/5=4/5
Since A, B, C are independent events
∴ A', B', C' are also independent events

Let X be the event that problem is solved.
Problem can be solved if at least one of the three students solves the problem.
P(X) = P (at least one student solves the problem)
= 1 – P .........(no student solved problem)
= 1 – P (A' ∩ B' ∩ C')
= 1 – P(A') P(B') P(C')

= 1 - 2/3xx3/4 xx4/5

= 1 - 2/5

= 3/5

Concept: Independent Events
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