A machine operates only when all of its three components function The probabilities of the failures of the first , second and third component are 0.2, 0,3 and 0.5 respectively . What is the probability that the machine will fail ?

Options

A. `0.70`
B. `0.72`
C. `0.07`
D. none of these

Answer

B

Explanation

Let `E_(1),E_(2) " and "E_(3)` be the events that the 1st 2nd and 3rd component function . Then
`P(E_(1))=(1-0.2) =0.8 P(E_(2)) =(1-0.3) =0.7 " and " P(E_(3)) =(1-0.5) =0.5`
P(machine fails) =1- P(machine functions)
`=1-P(E_(1) ,E_(2) " and " E_(3)) =1- {P(E_(1)) xx P(E_(2))xx P(E_(3))}`
`=1- (0.8xx 0.7 xx 0.5)=(1-0.280 )=0.72`