Stanford University (25pts.) In the city of Cincinnati there are two taxicab companies, the Yellow and the Orange. As you may suppose, the Yellow cabs are yellow and the Orange cabs are orange. The Yellow Compay operates 400 cabs in the city and the Orange Company operates 40 cabs. One dark evening, a pedestrian is killed by a hit-and-run taxicab. There was one witness to the accident. In court, the witness' ability to distinguish cab colors in the dark is questioned, so he is tested under conditions similar to those in which the accident occurred. When he is shown an orange cab, he says it is orange 95% of the time time and yellow 5% of the time. When he is shown a yellow cab, he says it is yellow 80% of the time and orange 20% of the time. The judge believes that the test accurately represents the witness performance at the time of the accident, so the probabilities he assign to the events of the accident agree with the frequencies reported by the test.

Flip the tree. Label all endpoints, supply all branch probabilities, and calculate and label an endpoint probabilities.