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A Problem is Given to Three Students Whose Chances of Solving It Are 1/4, 1/5 and 1/3 Respectively. Find the Probability that the Problem is Solved. - Mathematics

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Sum

A problem is given to three students whose chances of solving it are `1/4, 1/5` and `1/3` respectively. Find the probability that the problem is solved.

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Solution

Let P(A) =`1/4 , "P"(bar"A") = 1 - 1/4 = 3/4`

P(B) = `1/5 , "P"(bar"B") = 1 - 1/5 = 4/5`

P(C) = `1/3 , "P"(bar"C") = 1- 1/3 = 2/3`

Probability (the problem is solved)

`= 1 - "P"(bar"A")."P"(bar"B")."P"(bar"C")`


`= 1 - 3/4 xx 4/5 xx 2/3`


`= 1 - 2/5 = 3/5`

Concept: Introduction of Probability
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