any help would be appreciated...thank you

[d1truth]

1.A smoke detector system uses 2 devices, A and B. If smoke is present, the probability that it will be detected by device A is .95, by device B is .90, and by both devices is .88

a.If smoke is present, find the probability that the smoke will be detected by either device A or B or both devices.

b.Find the probability that the smoke will be undetected.



2.Show that the additive law of probability, holds for conditional probabilities.


3.If A, B, C are 3 events, prove that P A or B or C is greater than or equal to 1 - P(A compliment) - P (B compliment) - P(C compliment)

 

[tkhunny]

1.A smoke detector system uses 2 devices, A and B. If smoke is present, the probability that it will be detected by device A is .95, by device B is .90, and by both devices is .88

a.If smoke is present, find the probability that the smoke will be detected by either device A or B or both devices.

b.Find the probability that the smoke will be undetected.

A Only: 0.95*(1-0.90)
B Only: (1-0.95)*0.90
Both: 0.95*0.90
Neither: (1-0.95)*(1-0.90)

After constructing the ENTIRE distribution, you should be able to answer any number of questions rather quickly.