You have are offered a contract on a piece of land which is worth 1000000 70% of the time, 500000 20% percent of the time and 150000 10% of the time. The contract says you can pay x dollars for someone to determine the land's value from where you can decide whether or not to pay 300000 for the land. What is x? I.e. how much is this contract worth?
Suppose you have two covariance matrices A and B. Is AB also a covariance matrix? Suppose that, by plain dumb luck, we also have that AB=BA. Is AB a covariance matrix under this additional condition?
What is the fastest amount of time you can get 4 people across a bridge. Each person takes a different amount of time .. 1 minute, 2, 5, and 10. They can cross 2 at a time but need a flashlight to cross.
Why are you interested in Network Rail and the graduate scheme?
Expected value of heads and tails of two coin flips -> E(t(10-t) = 10E(t) - E(t^2) = 50 - (25 + 10/4) = 22.5 What is the set of numbers between 2 and 30, without the same common factor (e.g. 26 and 24 share 2, so they cannot be in the same set) that will you give you a max sum? Using the same rules, what is the highest possible number you can have in a set of 1000?
Say I take a rubber band and randomly cut it into three pieces. What's the probability that one of the pieces has length greater than 1/2 of the original circumference of the rubber band.
I have a square, and place three dots along the 4 edges at random. (1) What is the probability that the dots, when connected, do not form a triangle? (2) what is the probability that the dots lie on distinct edges?
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?
roll a 30-sided die (Number 1-30) many times and add all up the outcomes. stop rolling when the sum >= 300. what's the most likely result of the sum?
How many times does the digit 1 appear in all numbers from 1-1000000 inclusive
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