# Probability

## 3 Baskets And 4 Balls Puzzle

Puzzle: You have 3 baskets and each basket contains exactly 4 balls, each balls is of the same size. Each ball is either red, black, yellow, or orange, and there is one of each color in each basket. If you were blindfolded, and lightly shook each basket so that the balls would be randomly distributed, Read More →

## Probability of getting one rupee coin from bag

Problem: A bag contains (x) one rupee coins and (y) 50 paise coins. One coin is taken from the bag and put away. If a coin is now taken at random from the bag, what is the probability that it is a one rupee coin? Answers: Case I: Let the first coin removed be one Read More →

## Probability of finding a job

Problem: A candidate is selected for interview for 3 posts.The number of candidates for the first, second and third posts are 3,4 and 2 respectively. What is the probability of getting at least one post? Solution: The probability the candidate does not get an offer from the first interview is 2/3. The probability she doesn’t Read More →

## Probability of picking 2 socks of same color

Problem: There are 6 pairs of black socks and 6 pairs of white socks.What is the probability to pick a pair of black or white socks when 2 socks are selected randomly in darkness. This question was asked in Aamaon. Solution: Ways to pick any 2 socks from 24 socks = 24C2 Ways to pick Read More →

## Red and Blue Marbles Puzzle

Puzzle: You have two jars, 50 red marbles and 50 blue marbles. You need to place all the marbles into the jars such that when you blindly pick one marble out of one jar, you maximize the chances that it will be red. When picking, you’ll first randomly pick a jar, and then randomly pick Read More →

## Generate integer from 1-8 with equal probability

Problem: Write a method to generate a random number between 1 and 8, given a method that generates a random number between 1 and 3. The distribution between each of the numbers must be uniform. Solution: Let’s think of this like a decision tree. Each rand3() will be a decision. If we somehow generate integers Read More →

## 3 Doors and Angel

Problem : You are given a choice of three doors by an Angel. You can choose only one of the doors among the three. Out of these three doors two contains nothing and one has a jackpot. After you choose one of the doors angel  reveals one of the other two doors behind which there Read More →

## 3 Doors and Heaven

Problem: A person dies, and he arrives at the gate to heaven. There are 3 doors in the heaven. One of the door leads to heaven, second one leads to a 1-day stay at hell and then back to the gate and the third one leads to a 2 day stay at hell and then Read More →

## Boys and Girls

Question: In a country where everyone wants a boy, each family continues having babies till they have a boy. After some time, what is the proportion of boys to girls in the country? (Assuming probability of having a boy or a girl is the same) Answer: “very simple”. Half the couples have boys first, and Read More →

## Ant and Triangle Problem

Puzzle: Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide? Puzzle Solution: So let’s think this through. The ants can only avoid a collision if Read More →