Bob\'s cube mate sees Bob coming in late to work on a morn bicycle, and uses it

Question

Bob's cube mate sees Bob coming in late to work on a morn bicycle, and uses it 70% of the time. The cube mate also knows that Bob is more likely to be late when he takes his car when he take the train and have only a 4% chance of being late. Given that Bob is late, what is the pro terms with one decimal point of precision.) ing that he was supposed to be a part of an important meeting. Bob's cube mate know that Bob prefers his if he takes his car. In fact, Bob has a 50% probability of being late does take his bicycle, he only has a 20% of being late if he does. He can also take the bus and have a 89 chance of being late, or bability that he took car to work? (Give your answer in percentage Answer 0.67 X (24.8)

Explanation / Answer

We are given here that:

P( bicycle ) = 0.7 and therefore P( car ) = 1 - 0.7 = 0.3

P( late | car ) = 0.5

P( late | bicycle ) = 0.2

P( late | bus ) = 0.08

P( late | train ) = 0.04

Using law of total probability, we get:

P( late ) = P( late | car )P( car ) + P( late | bicycle ) P( bicycle )

P( late ) = 0.5*0.3 + 0.2*0.7 = 0.29

Given that bob is late, probability that he took car to work is computed as:

P( car | late ) = P( late | car )P( car ) / P( late ) = 0.5*0.3 / 0.29 = 0.52

Therefore 0.52 is the required probability here.

Note that we cannot have answer in BLUE as the correct answer because the probability is always less than 1.

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