Question 2 (1 point) Bob\'s cube mate sees Bob coming in late to work on a morni

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Question 2 (1 point) Bob's cube mate sees Bob coming in late to work on a morning that he was supposed to be a part of an important meeting. Bob's cube mate know that Bob prefers his bicycle, and uses it 70% of the time. The cube mate also knows that Bob is more likely to be late if he takes his car. In fact, Bob has a 50% probability of being late when he takes his car. when he does take his bicycle, he only has a 20% of being late if he does. He can also take the bus and have a 8% chance of being late, or take the train and have only a 4% chance of being late. Given that Bob is late, what is the probability that he took car to work? (Give your answer in percentage terms with one decimal point of precision.) Your Answer: Answer Save

Explanation / Answer

Ans:

Given that

P(bicycle)=0.7

P(car)=0.1

P(bus)=0.1

P(train)=0.1

P(late/bicycle)=0.2

P(late/car)=0.5

P(late/bus)=0.08

P(late/train)=0.04

Now,

P(late)=0.2*0.7+0.5*0.1+0.1*0.08+0.1*0.04

Plate)=0.202

P(car/late)=P(late/car)*P(car)/P(late)

=0.5*0.1/0.202

=0.248 or 24.8%

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