The probability that a city bus is ready for service when needed is 84%. The probability that a city bus is ready for service and has a working radio is 67%. 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.
To find the probability that a bus has a working radio given that it is ready for service, we can use the formula for conditional probability:
P(working radio | ready for service) = P(working radio and ready for service) / P(ready for service)
Given data:
P(ready for service) = 0.84
P(working radio and ready for service) = 0.67
Plugging these values into the formula:
P(working radio | ready for service) = 0.67 / 0.84
P(working radio | ready for service) = 0.7976
Rounded to the nearest tenth of a percent, the probability that a bus chosen at random has a working radio given that it is ready for service is 79.8%.