If we play a game and you get paid for the number you role on a six sided die, what would you pay to play this game?
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You need to roll a dice for a high score. If you roll it once, and you are not satisfied about it you can roll it another time. But you need to keep the second number. What is the expected value?
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If i roll two dice, what is the probability that the second is higher than the first?
1. Digits in 99^20 2. Expected value of dice rolls (20 x 3 vs. 30 x 2). If you were playing a game which one would you pick, or does it not matter? What's the probability that you're going to win?
Have a truck starting that can carry a maximum of 1000 apples, and starts with 2000 apples at a depot. What's the maximum number of apples that can be carried across a 1000 mile desert assuming 1 apple falls off the truck for every mile travelled?
Ask you to find the smallest number that you can not get by using 3,8,20 (or something similar)
if you have a 6 by 6 matrix where each element is either 1 or -1, how many unique matrices are there such that each row and each column multiplies to 1.
You play a game where you roll a 100-sided die label with the numbers 1-100. You can either get paid the amount rolled in dollars or pay a dollar to roll again. You can always elect to pay another dollar to roll again, until you're finally satisfied with your current roll and get paid out based on that. What's the optimal strategy for this game and what's your expected winnings given this strategy?
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