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Every character is known but password is hard to crack
In this post, we discusses an example in which you are given a password (every character of it) and yet it is still very hard (or even impossible) to crack. Anyone who understands this example has a...
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How long does it take to collect all coupons?
This post discusses the coupon collector problem, a classical problem in probability. ___________________________________________________________________________ The Coupon Collector Problem The...
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The birthday problem
Consider this random experiment. You ask people (one at a time) of their birthdays (month and day only). The process continues until there is a repeat in the series of birthdays, in other words, until...
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Are digits of pi random?
What better way to celebrate Pi Day than to have a blog post on the digits of ! Giving pi as tips The number is the ratio of the circumference of a circle to its diameter. It is an irrational number....
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The gambler’s ruin problem
This post discusses the problem of the gambler’s ruin. We start with a simple illustration. Two gamblers, A and B, are betting on the tosses of a fair coin. At the beginning of the game, player A has 1...
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Monty Hall Problem
The post discusses the Monty Hall problem, a brain teaser and a classic problem in probability. The following 5 pictures describe the problem. Several simple solutions are presented....
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More about Monty Hall Problem
The previous post is on the Monty Hall Problem. This post adds to the discussion by looking at three pieces from New York Times. Anyone who is not familiar with the problem should read the previous...
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The Gamma Function
A student in a probability course may have evaluated an integral such as the following: Plug in a value for and evaluate the integral. For example, when evaluated at , the integral has value 1....
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Bayes’ formula gives better perspective on medical testing
Suppose that a patient is to be screened for a certain disease or medical condition. There are two important questions at the outset. How accurate is the screen or test? For example, at the outset,...
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Probability problems using Markov chains
This post highlights certain basic probability problems that are quite easy to do using the concept of Markov chains. Some of these problems are easy to state but may be calculation intensive (if not...
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