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Four persons independently solve a certa...

Four persons independently solve a certain problem correctly with proabilities `1/2,3/4,1/4,1/8.` Then the probability that the problem is solved correctly by at least one of them is

A

`(235)/(256)`

B

`(21)/(256)`

C

`(3)/(256)`

D

`(253)/(256)`

Text Solution

Verified by Experts

The correct Answer is:
A
PLAN It is simple application of independent event , to solve a certain problem or any type of compitition each event in independent of other .
Formula used
`P(A cap B )=P(A)*P(B)` , when A and B are independent events .
Probability that the problem is solved correctly by atleast one of them =1- (problem is not solved by all )
` :.` P(problem is sovled ) =1- P(problem is not solved )
`=1-P(bar(A)) *P(bar(B))*P(bar(C))*P(bar(D))`
`=1-((1)/(2) *(1)/(4) *(3)/(4) *(7)/(8))=1-(21)/( 256) =(235)/(256)`
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