A cab was involved in an accident and ran away. An eyewitness to the accident claims that the cab was yellow. Knowing that eyewitness tell the truth in only 75% of the cases, the police officer decides to ask a second independent witness about the accident. The second witness also reports that the cab was yellow.

1. Compute a new probability that the cab was yellow given two independent witnesses claiming that the cab was yellow. (Draw Tree Diagram)

2. In one or two sentences, explain the significance of the fact that the second witness is independent of the first witness. How does this impact your calculation of the probability that the cab was indeed yellow?