Probability Notes

Sample Space

A Sample Space for an event is the set of all possible outcomes of that event.

Example: What is the Sample Space for flipping three coins?

It is the set containing {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}.

Notice that HHT is a different outcome than HTH, where H= Heads and T=Tails. The reason it is different is that different coins are giving me different results. Take a look at the second coin. It is coming up heads in the first case and tails in the second. Since the same coin has different results it has to be a different outcome.

For Sample Space the ORDER of multiple outcomes matter.

Sometimes sample space can be written out using a tree diagram below.

Notice that following each branch gives a different outcome.

Now of course, the more possibilities can make this diagram too big. Also writing out the sample space crazy. So there has to be an easier way of finding the number of possible outcomes, which is needed for probability, easier than writing out what each outcome is.

Enter COMBINATORICS!