## Probability puzzles

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?

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Solution
Source: Written Test
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Roll a die, and you get paid what the dice shows. But if you want, you can request a second chance & roll the die again; get paid what the second roll shows instead of the first. What is the expected value?

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?

Hint
Solution
Source: Self, to show an example of recursive probability
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What is the expected number of coin tosses required to get n consecutive heads?

Hint
Solution
Source: Top Quant Interview
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A chess tournament has K levels and 2^K players with skills 1 > 2 > ... >2^K. At each level, random pairs are formed and one person from each pair proceeds to next level. When two opponents play, the one with better skills always wins. What is the probability that players 1 and 2 will meet in the final level?

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Solution

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