There are 100 coins and someone flips them and doesn't tell us the results. I can ask one Yes/No question. After the answer I will start guessing the coin flip results. For each correct guess I get 1 dollar and for each wrong guess I lose 1 dollar. What is the best strategy to play this game and what is the maximum expected value of the return.
Q1: We have two integers A and B and we know A/B is in the interval [0.48, 0.52]. What are all possible values for B?
rolling 2 dices, case 1 you will earn $1 is sum of them are 7; case 2 earn -$1 is sum of then are even; otherwise, roll them again until case 1 or 2 happen. Find the expected gain.
a/b within 0.48 0.52 a,b are both integers . What could a and b be
4 coin flips, probability of at least 2 heads
If rolling two dice, probability of rolling a square number (1,4,9,..)
To present one of my UX cases
On the second call, I was asked this. You roll a 100-side dice and get paid the number it shows. However, you can roll again for the price of 1 pound (you get paid once only on the last roll). What is your strategy to maximize profit?
The questions were the usual ones, the difference was in the non-verbal response of the interviewers.
1. 2 players, 30 sided die. A choose the number first and B then choose a different number. The one who choose the number which is closer to the number the die rolls wins the amount (the die rolls) of money. For example, A choose 9, B choose 10, if die rolls 7 then B pay A 7 dollars. Would you like to be A or B? What number would you choose? What is your expected return? Does your strategy depend on you opponent?
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