Probability of Compound Events

Sample Space: Mapping All Possibilities

What if I told you that before any game show contestant spins the wheel or picks a door, mathematicians can already map out every single thing that could possibly happen? This complete map of possibilities is called the sample space.

Think of sample space like creating a master list of every possible outcome before an event happens. For simple events like flipping one coin, it's easy: {Heads, Tails}. But when we combine events—like flipping two coins or rolling a die AND picking a card—things get more interesting.

Building Sample Spaces Step by Step

Let's say you're choosing an outfit: you can pick from 2 shirts (Red or Blue) and 3 pairs of pants (Jeans, Khakis, or Shorts). How many different outfit combinations are possible?

We can organize this using a table to see every possibility:

Our complete sample space is: {(Red, Jeans), (Red, Khakis), (Red, Shorts), (Blue, Jeans), (Blue, Khakis), (Blue, Shorts)}. That's 6 total outcomes!

Lists vs. Tables: Choosing Your Tool

For simple compound events, an organized list works great. For more complex situations with multiple categories, tables help you stay organized and ensure you don't miss any outcomes. Both methods give you the same complete picture—they just organize the information differently.