How to solve the following problems?
1. X throws a coin for 3 times. If he gets a head all the 3 times he is to get a price of $200. The entry fee for the game is $24. Find the expectation of X. (ans. $4)
2. X and Y with equal skill leave a game when X scores 12 points and Y 13 points. If the game was to finish at 15, what is their respective probability of winning? (ans. 5/16, 11/16)
3. X, one of the 5 horses entered into a race and is to be ridden by one of the 2 jockeys A and B. It is 3:1 that A rides X, in which case all the horses are equally likely to win. If B rides X, his chance is doubled. What are the odds in favour of its winning? (ans. 1:3)
4. X has 4 shares in a lottery in which there are 4 prizes, and 5 blanks. Y has 3 shares in another lottery in which there are 3 prizes and 4 blanks. Who has the better chance of winning exactly one prize? And who of winning 2 prizes?
5. If on an average 1 out of 10 vessels is worked, find the probability that out of 5 vessels expected to arrive, 4 at least will arrive safely? (ans. 0.92)