Bob\'s cube mate sees Bob coming in late to work on a morn bicycle, and uses it
ID: 3359760 • Letter: B
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.