Anyway have some brain teasers they got on interviews and want to share?
Probability Brainteasers in an S&T Interview
One user, @CUQTrader, shared a good list of trading brainteaser interview questions.
- Classic one: I can roll a die and collect the amount of money on the die, or if I don't like it, I can roll a second time and I have to pick up the die. What is my expected value?
- There is a number line 0 to 10. A random number will be randomly generated over that line and you'll get paid that much. Would you rather the numbers be on the real line or all integers?
- I like the numbers 4 and 5. I also like any number that can be added together using 4s and 5s. I.e. 9 = 4+5. 40 = 5 + 5 + 5 + 5 + 5 + 5 + 5 +5. How many number have this property from 1 to 1000?
- There is a magic island with 85 lions and 1 sheep. what makes the island magical is that all animals could live on the island only by eating grass. however, the lions would like to eat the sheep. However, when one lion eats the sheep, the sheep dies naturally, and then the lion turns into the sheep. If everyone were to act naturally how many animals would there be on the island?
- You have 100 quarters in a jar. One of the quarters is double sided (heads). You pick out a random quarter and flip it 7 times, and get all heads. what is the probability you picked the double sided quarter? Then, given that you flipped it 7 times with all heads, what is the probability that you'll get heads on the 8th flip?
Answer: Given that the expected value of one roll is 3.5, you would only re-roll for a second round if you roll is below 3.5-- So that is, you would only keep the first roll if it's 4, 5 or 6. Note that you would re-roll 50% of the time. The expected value of your first roll is therefore 5. The expected value of 2nd roll alone is 3.5. Answer: 1/2 (3.5 + 5) = 4.25
Answer: If 0 and 10 are included, the expected value for both is 5.
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