I) I have just tossed a fair coin 7 times. Guess which of the four sequences below is genuine (order them according to their plausibility):
II) A die has been painted in such way so that it has four green faces and two red. I have thrown the die repeatedly into a table and produced one of the four sequences. Which one is the genuine one (please order them according to their plausibility)?
You are a member of a jury. A taxi driver is accused of having run down a pedestrian on a stormy night and having fled the scene of the accident. The prosecutor, in asking for a conviction, bases his whole case on a single witness, a lady who saw the accident from her window a little way away. The lady testifies that she saw the pedestrian struck by a blue taxi and then saw that taxi drive away from the scene of the accident. The accused works for a taxi company whose taxis are all blue. During the trial the following emerges:
1. There are only two taxi companies in this town. The whole fleet of one company is green; the other has only blue cabs. Eighty-five percent of all taxis on the road that night were green, and only 15 percent were blue.
2. The single witness has undergone a number of vision tests in conditions similar to those of the night of the accident. She has been shown to be able to distinguish a blue taxi from a green on 80 percent of the time.
On the basis of the sworn testimony of the witness, and the data offered in 1 and 2, what is the probability that the taxi was really blue?
What say you jury?
Please do not cheat 🙂
Source: The interesting book of Massimo Piattelli-Palmarini, Inevitable Illusions: How Mistakes of Reason Rule Our Mind