Probability
Lessons in this chapter
About Probability
Probability introduces the likelihood of an event happening as a number between 0 and 1, then teaches two different ways to find that number and how to combine more than one event at once.
Understand probability establishes probability as a number from 0 (impossible) to 1 (certain), usually written as a fraction, decimal, or percent, describing how likely a specific outcome is.
Find theoretical and experimental probabilities distinguishes between the two main ways to determine a probability: theoretical probability is calculated from the possible outcomes before anything happens (like a 1-in-6 chance of rolling a specific number on a die), while experimental probability is based on the actual results of repeating a trial — like the outcomes of 100 real rolls — and the chapter has kids compare the two to see how experimental results approach the theoretical value as trials increase.
Find the probability of compound events extends single-event probability to two or more events happening together — like flipping a coin and rolling a die at once — introducing how to count every possible combined outcome and use it to calculate the probability of a specific combination.
Frequently asked questions
A probability of 0 means an event is impossible — it will never happen — and a probability of 1 means it’s certain — it will always happen. Understand Probability places every other probability somewhere on that 0-to-1 scale, so an event with probability 0.5 is exactly as likely to happen as not.
Theoretical probability is calculated ahead of time from the possible outcomes, assuming everything is fair — like reasoning that a fair six-sided die has a 1-in-6 chance of landing on any given number. Experimental probability is based on what actually happened over a number of real trials, like the actual results of rolling that same die 60 times.
Divide the number of favorable outcomes by the total number of possible outcomes — for a fair six-sided die, the theoretical probability of rolling a 4 is 1 (favorable outcome) divided by 6 (total possible outcomes), or 1/6. Find Theoretical and Experimental Probabilities has kids apply this to dice, coins, spinners, and other equally-likely-outcome situations.
Divide the number of times an outcome actually occurred by the total number of trials performed — if a die is rolled 60 times and lands on 4 a total of 12 times, the experimental probability of rolling a 4 is 12/60, or 1/5. This is calculated from real data, not predicted ahead of time.
Randomness means individual results vary — even with a perfectly fair die, 60 rolls won’t always land on each number exactly 10 times. Find Theoretical and Experimental Probabilities has kids notice that as the number of trials increases, the experimental probability tends to get closer to the theoretical probability, a pattern worth seeing in real data rather than just being told about.
A compound event combines two or more separate events happening together, like flipping a coin AND rolling a die in the same trial, rather than looking at just one event alone.