Question

To get to school you can travel by car, bus or bicycle. If you travel by car, there is a 50% chance you will be late because the roads are very busy. If you travel by bus, which uses special reserved lanes and the busway, the probability of being late is only 20%. If you travel by bicycle you are only late 1% of the time.

(a) Suppose that you are late one day to class. Since your teacher does not know which mode of transportation you usually use, he assumes each of the three possibilities are equally likely. If you are late, find the probability that you travelled to school that day by car?

(b) Suppose that a friend tells your teacher that you almost always ride your bicycle to school, never take the bus, but 10% of the time travel by car. If you are late, what is the new probability that you travelled to school that day by car?

Answer 1

a) 16.66%

b) 5%

Explanation:

a)

Since the teacher assumes each of the three possibilities are equally likely, then he assumes 33.33% to each one.

In this case the probability that you traveled to school that day by car would be

50% of 33.33% = (0.5)(0.3333) = 0.1666 = 16.66%

b)

In this case, the teacher would assume

90% ride on bicycle

0% take the bus

10% travel by car

So, in this case the probability would be

50% of 10% = (0.5)(0.1) = 0.05 = 5%