Tag: probability

Thomas Bayes’ theorem and “inverse probability”

The following is an excerpt from Cautionary Tales in Designed Experiments by David Salsburg. This book is available to download for free from SAS Press. The book aims to explain statistical design of experiments (DOE) to readers with minimal mathematical knowledge and skills. In this excerpt, you will learn about […]

Thomas Bayes’ theorem and “inverse probability” was published on SAS Users.

What are the odds of … winning the lottery?

What are the odds of winning the lottery?  This seems like a simple question (and yes, there is a simple answer), but there are a few technical details to work out first… Which lottery?  Let’s say the Powerball Lottery. When? The number of balls us…

Example 9.21: The birthday "problem" re-examined

The so-called birthday paradox or birthday problem is simply the counter-intutitive discovery that the probability of (at least) two people in a group sharing a birthday goes up surprisingly fast as the group size increases. If the group is only 23 peo…

Example 8.36: Quadratic equation with real roots

We often simulate data in SAS or R to confirm analytical results. For example, consider the following problem from the excellent text by Rice:Let U1, U2, and U3 be independent random variables uniform on [0, 1]. What is the probability that the roots…