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Answer to Question #15542 in Statistics and Probability for sanio123

Question #15542
Carol lives in the east end of Montreal. To get to school for her morning classes Carol has the option of taking the bus, going underground with the metro, or driving her car downtown to get to School. Carol prefers the metro, especially in the winter, and she will opt for it 50% of the time. The bus is perhaps a more convenient option since it stops near her house, so she will choose that option 40% of the time. The car is the most expensive option, but it is the most reliable, as demonstrated by the fact that she is only late for class 5% of the time when she drives. The bus is the least reliable of the options as it gets Carol to class on time 70% of the time, whereas this value increases by 10% with the metro.
d) What is the probability that Carol opted for the bus given that she was late to class?
e) What is the probability that Carol is onā€time for class given that she did not drive?
Expert's answer
At first we will calculate the probability for Carol being late for class/ It's as follows
0.5*0.6+0.4*0.7+0.1*0.05=0.585
Now, using the formula for conditional probability we get P(bus|being late)=
=P(bus&being late)/P(being late)=0.4*0.7/0.585=0.479
P(on time|not drive)=P(on time&metro)+P(on time&bus)=0.5*(1-0.6)+0.4*(1-0.7)=0.32

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