Jane and Joe live on either side of Jack’s house. Jack loves to collect data on

Question

Jane and Joe live on either side of Jack’s house. Jack loves to collect data on his various neighbors. His latest data collection effort consisted of observing the mode choices of Jane and Joe each morning. After many weeks of observation, he found that there is a 3/5 probability that Jane takes the subway to work. Joe, on the other hand, takes the subway with probability 1/4. The only other alternative that they have available to them is driving their own cars to work. Jack also noticed that Jane and Joe always depart at the same time. By talking with Jane and Joe independently, Jack discovered one day that they even work in the same office building and get off work at the same time as well. This made him wonder about the possibility of carpooling. What is the probability that Jane and Joe carpool on a particular day assuming that they elect to carpool only if each of them independently decides not to take the subway that day?

Explanation / Answer

P(Jane take Subway ) = 3/5

P(Jane not to take subway) = 1-3/5 = 2/5

P(Joe take subway)= 1/4

P(jane not to take subway) = 1-1/4 = 3/4

P(jane and joe car pooled ) = P(jane not to take subway)*P(joe not to take subway ) = (2/5)*((3/4) = 3/10

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