Four persons can hit a target correctly with probabilities `(1)/(2),(1)/(3),(1)/(4)` and `(1)/(8)` respectively. If all hit at the target would be hit, is

Options

A. `(1)/(192)`
B. `(25)/(32)`
C. `(7)/(32)`
D. `(25)/(192)`

Answer

B

Explanation

Key Idea Use `P(bar(A)) =1-P(A)` and condition of independent events i.e. `P(A cap B)=P(A) *P(B)`
Given that probability of hitting a target independently by four persons are respectively
`P_(1)=(1)/(2),P_(2)=(1)/(3),P_(3)=(1)/(4) and P_(4)=(1)/(8)`
Then , the probability of not hitting the target is
`=(1-(1)/(2))(1-(1)/(3))(1-(1)/(4))(1-(1)/(8)) " "` [` :.` events are independent ]
` =(1)/(2) xx (2)/(3) xx (3)/(4)xx (7)/(8)=(7)/(32)`
THerefore , the required probability of hitting the target =1- (Probability of not hitting the target)
`=1-(7)/(32) =(25)/(32)`