Four person independently solve a certain problem correctly with probabilities `1/2,3/4,1/4,1/8dot` Then the probability that he problem is solve correctly by at least one of them is

Options

A. `(235)/(256)`
B. `(21)/(256)`
C. `(3)/(256)`
D. `(253)/(256)`

Answer

A

Explanation

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)`