A few days ago I found someone asking an interview questions on mitbbs. The question is as follows. A gambler plays a fair game and bet 1 dollar each time. If he lose all his money, the game stops. Suppose he has 10 dollars and is only allowed to play …

The following is a popular brain teaser problem about probability.

Randomly select two points on a unit stick to break it into 3 pieces, what is the probability that the 3 pieces can form a triangle?

The critical thing here is how are the two points selected. The most popular …

Suppose a poker games requires 4 decks of poker. After the game, the cards are put back into the 4 decks randomly. Now there is another game which requires only 1 deck of poker, so we want to open some decks of the poker and find a complete set of …

There are \(N\) seats on a plane. Suppose the first passengers is drunk and he takes a seat randomly. For each of the other passengers, if his/her seat is not taken by other people, then he/she sits on his/her own seat, otherwise he/she takes a seat …

Suppose a basketball player make \(N\) shots, and we know that in the first \(n(\le N)\) shots he sinked \(m(\le n)\) shots. If from the \((n+1)^{th}\) shot, his ratio of sink a shot is his accumulative ratio before the shot, e.g., suppose he sinked 40 …

There are 100 seats on a plane. If each of the 100 passengers randomly take a seat, how many people will have his/her own seat on average?

There is a classic way to solve this problem, which is to decompose a (complicated) random variable into a sum of simple …