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2026-02-22 08:40:56 +00:00
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* p and q are two points chosen at random between 0 & 1. What is the probability that the ratio p/q lies between 1 & 2?
* A very innocent monkey throws a fair die. The monkey will eat as many bananas as are shown on the die, from 1 to 5. But if the die shows '6', the monkey will eat 5 bananas and throw the die again. This may continue indefinitely. What is the expected number of bananas the monkey will eat?
* What is the expected number of coin tosses required to get n consecutive heads?
* On Monday, a fair coin is flipped. If it lands as heads, you are awoken on Tuesday and Wednesday. If it lands as tails, you are awoken on Thursday. Whenever you are awoken, you are given the opportunity to buy a call option expiring Friday for a particular security. You have access to relevant data up to Monday, but are not told what day it is when awoken, and after each awakening your memory of that awakening is erased. How should you determine whether to buy the option?
* On Monday, a fair coin is flipped. If it lands as heads, you are awoken on Tuesday and Wednesday. If it lands as tails, you are awoken on Thursday. Whenever you are awoken, you are given the opportunity to buy a call option expiring Friday for a particular security: the parameters of this offer were fixed on Monday. You have access to relevant data up to Monday, but are not told what day it is when awoken, and after each awakening your memory of that awakening is erased. How should you determine whether to buy the option?