Probability puzzles




Medium Probability

Snow-particles are falling on the ground one after another. A particular snowflake turns out to be of type "Stellar Dendrite" with probability 'p' if its previous particle was also Stellar Dendrite, and with probability 'q' if previous one was something else. If a snowflake is picked from ground, what is the probability that it is Stellar Dendrite?

PS:Although no two snowflakes are alike, yet there are various crystalline structures to categorize their interesting shapes. The image depicts the most popular shape, called Stellar Dendrites, which means star-like particles with tree-like branches.

image

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Medium Probability

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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Source: Written Test
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Medium Probability

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?


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?

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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?

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Source: Top Quant Interview
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