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)

Question

Responses

77.6%
77.6%

17.0%
17.0%

58.1%
58.1%

79.8%

Answer 1

In this case, we can use the formula for conditional probability:

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

Where:
P(A | B) is the probability of A given B
P(A and B) is the probability of A and B both happening
P(B) is the probability of B happening

Given in the problem:
P(Bus is ready for service) = 0.76
P(Bus is ready for service and has a working radio) = 0.59

Now, let's plug these values into the formula:

P(Working radio | Ready for service) = 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 77.6% (rounded to the nearest tenth of a percent).