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.
Let A be the event that a city bus is ready for service and B be the event that the bus has a working radio.
We are given:
P(A) = 0.84
P(A and B) = 0.67
We want to find P(B|A), the probability that a bus has a working radio given that it is ready for service.
P(B|A) = P(A and B) / P(A)
P(B|A) = 0.67 / 0.84
P(B|A) ≈ 0.7976
Therefore, the probability that a bus chosen at random has a working radio given that it is ready for service is approximately 79.8%.