Suppose that Bob can decide to go to work by one of three modes of transportatio

Question

Suppose that Bob can decide to go to work by one of three modes of transportation, car, bus, or commuter train. Because of high traffic, if he decides to go by car, there is a 50% chance he
will be late. If he goes by bus, which has special reserved lanes but is sometimes overcrowded, the probability of being late is only 20%. The commuter train is almost never late, with a probability of only 1%. The probability that on any given day that Bob uses the car is 70%, the bus 20%, and the commuter train 10%. Withe probability that Bob is late?

Explanation / Answer

Ans:

Given that

P(late/car)=0.5

P(late/bus)=0.2

P(train)=0.01

P(car)=0.7,P(bus)=0.2,P(train)=0.1

Now,

P(late)=P(late/car)*P(car)+P(late/bus)*P(bus)+P(late/train)*P(train)

=0.5*0.7+0.2*0.2+0.01*0.1

=0.35+0.04+0.001

=0.391

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