suppose you have a perfectly round disk. You put three legs randomly on this disk to form a table. Supposing the legs are perfectly perpendicular to the disk and are attached to the disk firmly, what is chance that the table will not fall when you flip the disk or in other word when you put the table to stand on its legs?
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?
Suppose you have 100 GB of data that you want to sort, but you only have 1 GB of memory. How would you sort this data?
You have 100 marbles, 50 are blue, 50 are red. You want to distribute them between two drawers, in such a way that none is left outside and no drawer is left empty. After distributing them you are gonna select a drawer randomly and from that drawer you are gonna remove one marble randomly. How do you distribute the marbles in such a way that the probability of getting a red marble is maximized?
Unfair coin with P(H) = 1/3 and P(T) = 2/3. a) How to make an event with 50% probability? b) Expected number of flips until a realization occurs? c) Can you create a strategy to reduce the number of flips necessary? d) Can you create a strategy to reduce the number of flips necessary for an unfair coin with any bias?
suppose you live in middle town, your mom lives in downtown while your girl friend lives in uptown. You take subway to have dinner with either your mom or your girl friend every night. You always the first train that arrives at the station. why do you end up with have dinner with your girl friend 90% of the times? assume the uptown and downtown train run at the same intervals.
Given a thirty sided dice A and a twenty sided diced B, I win (a) dollars if a > b, and i lose (b) dollars if b >= a, what's they expected pay off
Write numbers 2^1000 and 5^1000 in a decimal notation, next to each other. How many digits does the newly obtained number have?
find a subset of {1,2,3,...,30} so that numbers in that subset is coprime to each other.
brainteaser: 30 people are 15 couples. they shake hands, but two people of the same couple don't shake hands with each other. now you know 29 people shake hands with different numbers of people (e.g. one person shakes hands with 4 others, another person shakes hands with 5 people, etc). question: how many people did the 30th person shake hands with?
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