SIG (Susquehanna) Interview Questions

What is the probability that a group of people sitting around a round table are seated in strictly ascending or strictly descending order of age?

There are different levels of smokers, with some being more likely to die than others. If a person has died, what is the probability that they were a heavy smoker?

You are betting $50 on a basketball game and your friend is betting $20. If you win, you gain your friend's $20; if you lose, you forfeit your $50 to your friend. What is your expected profit?

Pick three numbers between 1 and 20. What is the probability that one of the numbers is the average of the other two?

What is the probability of getting the sequence HHT before HTH when flipping a fair coin repeatedly?

You play a game where you have $100 to split between yourself and a random person. You decide how to split it, and the other person can either accept (so you both receive the split amounts) or refuse (in which case both of you get $0 and the game ends). What split do you propose? What if the amount to split is $1,000,000?

What is the probability of rolling six consecutive 3s with a fair six-sided die?

Suppose we have a $10 bet. At any time, I can ask to double the bet. If you accept, we both put in another $10, so the winner gets $20. If you lose, you forfeit everything; if you reject the double, you lose the initial $10. What is the minimum probability of winning that would make you accept the double?

Suppose you and I are playing a game and have bet $10, which will go to the winner. At some point, I offer to double the bet to $20. If you accept, the game continues with the new bet; if you refuse, you lose the game and forfeit the original $10. What is the minimum probability of winning that you would need to accept the increased bet?

You have two torpedoes to hit a boat. Each torpedo has a 2/3 chance of hitting the boat. If you launch both torpedoes, what is the probability that the boat is hit?

You can roll a fair six-sided die a maximum of two times. After each roll, you can choose to accept the current roll's value or roll again (if it is your first roll). You must accept the value on your last roll. What is the expected value of this strategy?