Probability puzzles




Medium Probability

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
Answer
Solution
Source: Self, to show an example of recursive probability
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Medium Probability

What is the expected number of coin tosses required to get n consecutive heads?

Hint
Answer
Solution
Source: Top Quant Interview
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Medium Probability

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?

Hint
Answer
Solution


Medium Probability

A coin is tossed 10 times and the output written as a string. What is the expected number of HH? Note that in HHH, number of HH = 2. (eg: expected number of HH in 2 tosses is 0.25, 3 tosses is 0.5)

Hint
Solution
Source: Placement Test
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Medium Probability

The stick drops and breaks at a random point distributed uniformly across the length. What is the expected length of the smaller part?

Solution
Source: Quant Interview
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