Toss 4 coins - probability of more than 2 heads - expected winnings if $1 for each heads - expected winnings if can re-toss 1 coin if chosen 1 20 sided die - player A and B both choose a number. Whoever's number closest to value of the die wins the amount on the die. - optimal strategy? do you want to go first? - what is the expected winnings?
You have a 3x3x3 cube painted yellow on the outside. The cube is then split up into 1x1x1 cubes. You pick one of these cubes at random and notice that the side you are looking at is painted. Without knowing if any of the other sides are painted, what is the probability that this was a corner cube?
Let's say you have 2 regular 6-faced dice. When you throw them down, you know the sum distribution (can vary from 2 to 12). Now let's say you were to erase the numbers on the faces of both the dice, and rewrite them with a new set of positive integers. Can you replicate the same sum distribution? If yes, how?
73 - 227? What's the probability that it rains on at least one of Saturday or Sunday if Saturday has a 60% chance of rain and Sunday has a 70% chance of rain? You have 2 fairly weighted dice. You and an opponent pick any integer one after the other. If your number is closer to the sum of the faces on the rolled dice, you win. Do you want to go first and what number do you choose? What's the probability of winning? You have 27 cubes with all faces painted white. You put them together into a 3x3x3 cube and paint the exterior blue. After breaking it back up, you pick a cube and put it on the table and the five visible faces are all white. What's the probability the non visible face is blue?
You are standing beside a road watching cars pass by. The probability that you see a car pass by in 1 minute is 1/4. What is the probability that you see a car pass by in 30 seconds?
10 lightbulbs in a row, on or off, no two adjacent lightbulbs can be on. how many combinations can we have? you may use a piece of paper
What's the angle between the two arms of a clock when it is at 2:30?
Calculate e^5 up to two decimal numbers without calculation
You and a friend are playing a game where a random number X, between 1 to 20 is chosen, and one of you will pick a number and then the other will pick a different number. The one that guesses the closer number wins X dollars. Should you choose to go first, and what number should you choose?
How many ways are there to partition 20 into prime numbers?
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