高频题（0）
1. Apple Orchard Tree States
In an apple orchard, trees have three states: not ripe, ripe, and overripe. The transition from state 1 to 2 follows a uniform distribution over the total time, and from 2 to 3 follows a uniform distribution over the remaining time. When should a visitor arrive at the orchard to see the maximum number of ripe apple trees? Assume the total time is 1, the time to go from state 1 to 2 is x, and from state 2 to 3 is y, with the visitor arriving at time t. x follows U(0,1) and y follows U(x,1). Maximize P(xt|x
2. Calculate the probability of odd sums in a magic square
Given a 3x3 grid (magic square) and the numbers 1-9, calculate the probability that the sum of the numbers in each row or column is an odd number.
3. Calculate the daily P&L of a portfolio
Calculate the daily Profit and Loss (P&L) of a portfolio.
4. Expected Number of Children Until Girls Outnumber Boys
A couple continues to have children until they have more girls than boys. What is the expected total number of children they will have?
5. Probability of Meeting on a Grid
Two people are walking towards opposite corners on a 4x4 grid. What is the probability that they meet at some point?
