Bob’s boss sees Bob coming in late to work on a morning that he was supposed to

Question

Bob’s boss sees Bob coming in late to work on a morning that he was supposed to be a part of an important meeting. Bob’s boss doesn’t know what mode of transportation Bob prefers, but he does know that Bob is more likely to be late if he takes his car. In fact, Bob has a 40% probability of being late when he takes his car. He can also take his bicycle, and only has a 10% of being late if he does. He can take the bus and have a 6% chance of being late, or take the train and have only a 3% 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.)

Explanation / Answer

Here' answer to the question with detailed explanation:

Choosing any of the 4 modes of transport = ,25

So, probabilty of becoming late is = P(chances of taking a particular vehicle)*P(chances of getting late on that vehicle)

P( Given Bob is late, him coming to work by car)

= .25* .40 / .25*(.40+.06+.10+.03)

= .6780 or 67.80%

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