Probability (1 Viewer)

[cutemouse]

As a part of strategic planning to reduce road accidents, police are using three different, independent methods to detect speeding motorists on a freeway.

The probability that a speeding motorist will be detected by a highway patrol officer is 1/3, by a fixed camera is 3/4, and by a mobile radar unit is 1/2

Calculate the probability that a speeding motorist will be detected.


Thanks

 

[Xcelz]

As a part of strategic planning to reduce road accidents, police are using three different, independent methods to detect speeding motorists on a freeway.

The probability that a speeding motorist will be detected by a highway patrol officer is 1/3, by a fixed camera is 3/4, and by a mobile radar unit is 1/2

Calculate the probability that a speeding motorist will be detected.


Thanks

never seen a question like this but i'll have a try.

so if the motorist is detected, they can be detected by all of them, by 2 of them or by 1 of them.

Caught by 3 of them
P (caught by all) = (1/3)X(3/4)x(1/2) = 1/8

Caught by 2 of them
P(caught by patrol and camera & not by radar unit) = (1/3)x(3/4)x(1/2) = 1/8
P(caught by patrol & radar but not camera)= (1/3)x(1/4)x(1/2) = 1/24
P(caught by camera & radar not patrol) = (2/3)x(3/4)x(1/2) = 1/4

Caught by 1 of them
P(caught by patrol & not others) = (1/3)x(1/4)x(1/2) = 1/24
P(caught by camera and not others) = (2/3)x(3/4)x(1/2)= 1/4
P(caught by radar and not others) = (2/3)x(1/4)x(1/2) = 1/12

Chance of being caught = (1/8)+(1/8)+(1/24)+(1/4)+(1/24)+(1/4)+(1/12)
= 11/12

Hope that's right. there may have been an error in my maths some where which u may have to find.