You have 10 mice and 1000 bottles of wine. You also have 24 hours before a party, and one of the bottles has been tainted with a slow acting poison, which takes 24 hours to kill a mouse. In the 24 hours you have remaining, how many bottles can you guarantee safe for human consumption (assume humans and mice react identically)? Assume the lethal dosage is insignificant relative to the size of the bottle.
Assume X_i ~ i.i.d. Unif(0,1). What is the expected length of a sequence that is monotonically increasing when drawn from the distribution?
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.
Wayfair is going to send 2 different catalogs to their customers. One of the catalogs costs 50 cents to make and is 50 pages long. The conversion rate for the catalog is 5% and each customer brings in 315 dollars. The second catalog costs 95 cents to make, is 100 pages long and each customer brings in 300 dollars from it. The profit margin is 30%. What should the conversion rate for the second catalog be to make at least the same amount of profit as the first one. After you find the conversion rate for the second one, there is a second part of the problem. Wayfair is planning to make a new catalog which is going to cost 10 cents more than the 100 page one. The more expensive catalog is going to be sent out to 20% of the customers while the remaining 80% are going to get the 100 page one. Assume the same 30% profit margin and 300 dollar profit from each customer. What should the conversion rate for the new catalog be in order to receive the same profit at the end?
Expected number of flipping coins of getting two consecutive faces.
Pretend 1% of the population has a disease. You have a test that determines if you have that disease, but it's only 80% accurate and 20% of the time you get a false positive, how likely is it you have the disease.
Case interview: basic business problem (if product X costs Capital One $4.00 per unit, with a $800 sunk cost, and we charge X amount of dollars along with a $10 annual fee, how many do we need to sell to break even, etc). Followed by a longer discussion of more complex problems that the situation might entail.
Tell me about the role of mortgage analyst or how they work.
25 hourses. Race them in a group of 5. Find the minimum number of race you need to conduct to find the top 3 hourses.
You have a 1 mile long x 1 mile wide private island that you wish to turn into a resort. A plane requires a 2-mile long runway to take off. What do you do?
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