Probability With The Binomial Distribution And Pascal's Triangle: A Key Idea In Statistics

What Is The Binomial Distribution?

The binomial distribution is one of the key ideas in statistics.  It calculates the probability of getting a certain number of an outcome, for instance you can use it to calculate the probability of rolling five 6's out of 20 dice rolled.  The binomial distribution finds applications in things such as predicting outcomes from elections, in gambling, and even on the game "Plinko" on the television game show "The Price Is Right"

How Is The Binomial Theorem Explained In This Book?

This book walks through how the binomial distribution works in a step by step fashion, starting with some simple flips of a coin, and building up to examples that have uneven probability, and examples where you need to calculate the binomial coefficient over a range of numbers.  I.e.  to calculate the odds of winning at least 51 hands of blackjack out of 100 played.

The first several examples are explained using Pascal's triangle, since it gives a good visualization of the probability of different binomial coefficients.  Later problems give examples using the binomial equation, since it is more versatile.

Other Key Topics In This Book

• Multinomial Equation - If you need to calculate the probability distribution for more than two events, you need the multinomial distribution, not the binomial distribution
  
• The Normal Approximation - The binomial distribution is great, but sometimes you need an answer with less calculation.  This shows how to get a very good answer using the normal curve, provided you have a sufficient number of events