Probability: Measuring How Likely an Event Is

Hey, I'm Lumi — and today we're going to figure out something you use every day without even realizing it: how likely is something to happen? Probability is a number that measures how likely an event is. It always lands somewhere on a scale from 0 to 1. - A probability of 0 means the event is IMPOSSIBLE — it will never happen. - A probability of 1 means the event is CERTAIN — it will always happen. - Everything in between is somewhere in the middle. Closer to 0 means unlikely; closer to 1 means likely; 0.5 means the event is as likely to happen as not happen. Before we calculate, here's one key idea: the full set of all possible outcomes is called the **sample space**. Every possibility goes in there — none are left out, and none are counted twice. Here's how you calculate probability: P(event) = (number of favorable outcomes) ÷ (total number of outcomes in the sample space) Let's try it with the bag I'm holding. It has 3 red tokens, 2 blue tokens, and 2 yellow tokens — 7 tokens total. That's our sample space: {red, red, red, blue, blue, yellow, yellow}. What is the probability of pulling out a red token? Favorable outcomes = 3 (the red tokens) Total outcomes in the sample space = 7 (all tokens in the bag) P(red) = 3 ÷ 7 ≈ 0.43 That's closer to 0.5 than to 0, so pulling red is a real possibility but still less likely than not. You can also write probability as a fraction (3/7) or a percent (about 43%) — they all mean the same thing. Not sure where to start on a new problem? First count every token (or item) in the bag to find the total — that number always goes on the bottom of the fraction. Then count only the ones you want — that goes on top.