You are given three envelopes, one of which contains $100 and the others contain nothing. You randomly pick one envelope but don’t open it. The interviewer then opens one of the other two envelopes and shows that it’s empty. Now you have a choice: stick with your original envelope or switch to the other unopened envelope. What should you do to maximize your chances of winning, and why?
It was something like two players flip coins until one gets three heads. They take turns. Given that I go first and get heads, what is the probability that I win.
Card games associated with expectation. Options introduced to hedge against risks.
What is the probability of getting an even number of heads when throwing a coin 9 times?
A blind auction for the outcome of a rolls, from 1-100. How should you bid? How should you bid if you have to bid first? What would be your strategy?
Some unique probaility and statisctics question
You flip a fair coin until you get heads. What is the expected number of flips?
You play a 100-round game: each round you can either roll a fair 20-sided die (uniform 1 to 20) or “lock in” the current face and collect that same reward for all remaining rounds. You must roll in the first round. What is your optimal stopping / locking strategy and expected value?
You are playing a game where you flip a coin 5 times. You win if three heads come up in the 5 coin tosses. You lose if three tails come up in the 5 coin tosses. If you win you get £1. If you lose you lose £1. Before each flip you can choose to either double the stakes from their previous value (if you win you get £2n and if you lose you lose £2n where n is the amount you get if you win beforehand) or keep them the same. Are you willing to pay £0.50 to play this game?
Two math questions. One probability focused coin game and one expected value.
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