Kid-friendly explanation
Likelihood tells how likely something is to happen. If something is very likely, it will probably happen, like the sun rising tomorrow. If something is unlikely, it probably will not happen, like rolling a 7 on a normal 6-sided die. Likelihood can be described with words or with numbers.
Step-by-step worked examples
Example 1 (younger grades): Likely, unlikely, certain, impossible
Imagine a bag with 4 red marbles and 1 blue marble. You reach in without looking and take 1 marble.
- Getting a marble from the bag is certain, because every object in the bag is a marble.
- Getting a green marble is impossible, because there are no green marbles in the bag.
- Getting a red marble is likely, because 4 out of 5 marbles are red.
- Getting a blue marble is unlikely, because only 1 out of 5 marbles is blue.
- If the bag instead held 2 red marbles and 2 blue marbles, getting red and getting blue would be equally likely, because each color makes up the same number of marbles.
Here, likelihood is described using words that compare how probable each outcome is.
Example 2 (upper grades): Likelihood as a probability number
A spinner is divided into 4 equal sections labeled A, B, C, and D. You spin it once. The sample space, which is the list of all possible outcomes, is {A, B, C, D}.
Because the sections are equal and the spin is fair, each outcome has the same likelihood. The probability of landing on A is:
Number of A sections / Total number of sections = 1 / 4 = 0.25.
This means the likelihood of landing on A is 0.25, or 25%. The same is true for B, C, and D. Each outcome is equally likely, because each has probability 0.25.
Now compare two events:
- Event 1: Landing on A or B. Probability = 2 / 4 = 0.5.
- Event 2: Landing on A. Probability = 1 / 4 = 0.25.
Event 1 has a greater likelihood than Event 2, because 0.5 is greater than 0.25.
Going deeper with likelihood
In probability, likelihood is expressed by a number between 0 and 1. A probability of 0 means the event is impossible, and a probability of 1 means the event is certain. Numbers in between, like 0.2 or 0.7, show different degrees of likelihood.
As students move into more advanced work, they use likelihood to compare events, to describe compound events (events made of two or more simple events), and to understand independent events, where one event does not change the likelihood of another. They also learn to use theoretical probability, based on what should happen, and experimental probability, based on what actually happens in repeated trials.
In high school, likelihood is often modeled with curves such as the normal distribution. For example, test scores that follow a normal distribution allow students to estimate the likelihood that a randomly chosen student scored within a certain range. In statistics, random assignment in experiments helps support the likelihood that a treatment, not some hidden factor, caused a difference between groups.
Common mistakes about likelihood
- Mistake 1: Thinking "likely" means the same as "certain." A likely event has a high probability but could still fail to happen, while a certain event has probability 1 and must happen every time under the same conditions.
- Mistake 2: Ignoring the total number of outcomes when comparing likelihoods. For example, saying that getting 1 blue marble from a bag of 2 marbles is less likely than getting 1 blue marble from a bag of 10 marbles, just because 10 is bigger. The correct comparison uses probabilities: 1/2 = 0.5 is more likely than 1/10 = 0.1.
- Mistake 3: Assuming that past outcomes change the likelihood in a fair situation. For instance, after flipping 5 heads in a row on a fair coin, a student might say tails is "due" and now more likely. In reality, each flip is independent, and the likelihood of heads or tails on the next flip is still 1/2.
How likelihood shows up in everyday life
Likelihood appears in many daily decisions. Weather forecasts talk about the likelihood of rain as a percentage. Games that use dice, spinners, or cards depend on the likelihood of different moves or scores. Even simple choices, like bringing a jacket based on how often it has been cold this week, involve an informal sense of likelihood.