The probability that a city bus is ready for service when needed is 76%. The probability that a city bus is ready for service and has a working radio is 59%. Find the probability that a bus chosen at random has a working radio given that is is ready for service. Round to the nearest tenth of a percent. (1 point) Responses 79.8% 79.8% 77.6% 77.6% 17.0% 17.0% 58.1%

1 answer

The formula to find the probability of both events happening is:

P(A and B) = P(A) * P(B|A)

Where P(A and B) is the probability that the bus is ready for service and has a working radio, P(A) is the probability that the bus is ready for service, and P(B|A) is the probability that the bus has a working radio given that it is ready for service.

Let's plug in the values we know:

P(A and B) = 0.59
P(A) = 0.76

Now we can rearrange the formula to solve for P(B|A):

P(B|A) = P(A and B) / P(A) = 0.59 / 0.76 ≈ 0.776

Therefore, the probability that a bus chosen at random has a working radio given that it is ready for service is approximately 77.6%.

So the answer is: 77.6%