Imagine that Monty has 100 doors with 99 goats and still only 1 car. Once you pick a door, he reveals 98 other doors with goats behind them. What is the probability that you win the car if you switch?
Neui and Grant play a tennis match with a ‘win by two’ rule: The first player to score two points more than the other wins. Suppose that Neui wins a point with probability \(p\), and that each point is independent. Find the probability that Neui wins the match.
A single bacteria sits in a petri dish. Each minute, it either splits into two with probability \(p\), or dies with probability \(1 - p\). Find the probability that the bacteria go extinct as a function of \(p\).
Be careful when considering the roots of the polynomial you find…