Question 302609: The probability that a city bus is ready for service when needed is 83%. The probability that a city bus is ready for service and has a working radio is 69%. Find the probability that a bus chosen at random has a working radio given that it is ready for service. Round to the nearest tenth of a percent.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a = bus ready for service
b = working radio
p(a) = probability of a = .83
p(a+b) = probability of a and b occurring simultaneously = p(a) * p(b) = .69
p(b|a) = probability of b given a.
p(b|a) = p(a+b) / p(a).
p(b|a) = .69 / .83 = .831325301
That's your answer.
If you look at it in terms of percentages, this is what is happening.
Assume there are 100 buses in total.
83 are in service.
69 out of the 83 have a working radio.
The percentage of buses ready for service that have a working radio is therefore 69/83 = .831325301 * 100% = 83.1325301%.
Since 83.1325301% of the buses ready for service have a working radio, the probability of getting a bus that has a working radio, given that the bus you have is ready for service, is .831325301.
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