James lives in San Francisco and works in Mountain View. In the morning, he has 3 transportation options (bus, cab, or train) to work, and in the evening he has the same 3 choices for his trip home. If James randomly chooses his ride in the morning and in the evening, what is the probability that he'll take the same mode of transportation twice?How do you do it??

Accepted Solution

      If James takes a bus in the morning then the probability P(bus-morning)= 1/3
If he takes the bus in the evening then it will be P(bus-evening)= 1/3

P(bus and bus) = P(bus-morning) x P(bus-evening) = (1/3) x (1/3) = 1/9
This is same for other mode of transportation. So...
P(cab and cab) = 1/9 and P(train and train) = 1/3

P(same mode) = P(bus and bus) + P(cab and cab) + P(train and train) = 1/9+1/9+1/9= 1/3