## Probability puzzles

In this gambling game, a player can buy a ticket for Rs 1 on any number from 1 to 6. Three identical and unfair dice are rolled. If the booked number appears on 0, 1, 2 or 3 dice, player wins Rs 0, 1, 2 or 3 respectively, without returning the original Rs 1. What is expected money you can win after buying a ticket for Rs 1?

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Source: 50 puzzles in prob
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A and B are in a team called AB, playing against C. If AB team wins it gets Rs 3, nothing otherwise.

Game is: A and B are placed in 2 separate rooms far away. A will toss a coin and B will also toss a coin; A will have to guess outcome of B's toss and B will guess A's. If both guesses are right, team AB wins Rs 3, nothing otherwise.
Should they play the game, by giving Rs 1 in start to C.

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Solution
Source: Top Quant Interview
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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.

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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?

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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?

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