Probability

1. Romeo and Juliet have agreed to meet for a date sometime between 9pm and 10pm. Each of them randomly picks a time within this interval and shows up and waits for the other for fifteen minutes. What is the probability that they will actually meet?

2. Suppose three assets A, B, C are such that the correlation coefficient of A and B is 0.9 and the correlation coefficient of B and C is 0.8. Is it possible for A and C to have correlation coefficient 0.1?

3. What is the probability that the fourth business day of the month is Thursday?

Brain teaser

1. One hundred tigers and one sheep are put on a magic island that only has grass. Tigers can eat grass, but they would rather eat sheep. Assume:

1. Each time only one tiger can eat one sheep, and that tiger itself will become a sheep after it eats the sheep.
2. All tigers are as smart as you and perdectly rational and they want to survive. So will the sheep be eaten?

2. There are 25 horses, each of which runs at a cosntant speed that is different from the other horses. Since the track only has 5 lanes, each race can have at most 5 horses. If you need to find the 3 fastest horses, what is the minimum number of races needed to identify them? Suppose you can only observed the order of the race horses. Which means you can not use time to measure the speed.