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 `(235)/(256)` b. `(21)/(256)` c. `3/(256)` d. `(253)/(256)`

Options

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

Answer

A

Explanation

Required probability
`=1-(1-(1)/(2))(1-(3)/(4))(1-(1)/(4))(1-(1)/(8))=1-(1)/(2)xx(1)/(4)xx(3)/(4)xx(7)/(8)`
`=1-(21)/(256)=(235)/(256)`