Answer:
B-91%
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: arriving home after 7 p.m.
Event B: getting home by bus.
When he chooses to get home by bus, he arrives home after 7 p.m. 25 percent of the time.
This means that
Because the bus is cheaper, he uses the bus 70 percent of the time.
This means that
Probability of getting home after 7 p.m.
70% of the time he uses bus, and by bus, he arrives arrives home after 7 p.m. 25 percent of the time.
100 - 70 = 30% of the time he uses the car, and by car, he arrives home after 7 p.m. 6 percent of the time.
So
What is the approximate probability that Matthew chose to get home from work by bus, given that he arrived home after 7 p.m.?
Rouding up, 91%.
So the correct answer is:
B-91%