1.) A taxicab was involved in a fatal hit-and-run accident at night. Two cab companies, The Green and The Blue, operate in the city. You are told that:
? 85% of the cabs in the city are Green and 15% are Blue
? A witness identified the cab as Blue
The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness was correct in identifying the color of the cab 80% of the time. What is the probability that the cab involved in the incident was Blue rather than Green?
2. In the carnival game known as chuck-a-luck, a player plays an amount E as an entrance fee, selects a number between one and six, and then rolls three dice. If all three dice show the number selected, the player is paid four times the entrance fee; if two dice shows the number, the player is paid three times the entrance fee, and if only one die shows the number, the player is paid twice the entrance fee. If the selected number does not show up, the player is paid nothing. Let X denote the player's gain in a single play of this game, and assume the dice are fair. Determine the probability function of X.
Probabilities are presented.