Q:
A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?
Answer & Explanation
Answer: C) 3/4
Explanation: Let A, B, C be the respective events of solving the problem and A , B, C be the respective events of not solving the problem. Then A, B, C are independent event
∴A, B, C are independent events
Now, P(A) = 1/2 , P(B) = 1/3 and P(C)=1/4
P(A)=12, P(B)=23, P(C)= 34
∴ P( none solves the problem) = P(not A) and (not B) and (not C)
= P(A∩B∩C)
= P(A)P(B)P(C) [∵ A, B, C are Independent]
= 12×23×34
= 14
Hence, P(the problem will be solved) = 1 - P(none solves the problem)
= 1-14= 3/4
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