What Is Probability?

Math probability really isn't all that different from how we use the term in English. Probability is the chance of something happening. It's communicated as a decimal or a percent, with a range of 0 (0%) to 1 (100%). If something has 100% probability, then it is "for sure." Something with 0% probability is a "no way, not at all."

Example: I have a bag with 100 marbles in it (and nothing else). I reach into the bag and pull one thing out. The probability that I have a marble in my hand is 100%; the probability that there is a kitten in my hand is 0%.

Make sense so far?

Those endpoints are easy. What about something that's neither "for sure" nor "no way"? It's still pretty simple. The probability of an event equals "success" outcomes divided by all possible outcomes.

Simply put, probability is the measure of the likelihood an event will occur.

You've most definitely dealt with probability before, whether it was a friend who said "I'll probably be at school tomorrow", or if it was a teacher who said "You will probably need to study for this test a week in advance."

Your friend may or may not be at school tomorrow, but they are leaning more towards attending. If your teacher advises you to study early, then that means the test will probably have a high difficulty.

In statistics, probability is a number between $0$ and $1$, where $0$ is impossibility and $1$ is certainly. The higher the probability of an event, the more likely that event will occur.

Right! Since $p$ is not $1$, but pretty close to one, we can say that the probability of this event happening is most likely.

Probability of $0.5$

Now, what if we have a $p = 0.5$? That is straight down the middle, so we can say that we have an equal chance of the two events occurring. This is most common in coin flips, where the probability of getting heads is $p = 0.5$ and the probability of getting tails is $p = 0.5$.

Calculating Probability

To calculate probability, you simply just take the number of desired outcomes, divided by the number of total outcomes. For example:

Let's say we have $7$ red flags and $4$ blue flags in a bucket. If I want to select a flag, what is the probability of us picking a red flag?

There are $7 + 4 = 11$ total flags in the bucket, meaning the probabilities of picking each kind of flag is:

Red Flag: $\frac{7}{11} = 0.64$

Blue Flag: $\frac{4}{11} = 0.36$

(Video) Probability

by Scratch Garden

In this video by Scratch Garden, you will get an introduction to probability.

As the video explains, probability helps us think through the likelihood of an event occurring. In other words, it is a way to represent the degree of uncertainty for an event. Follow along with the video examples of exploring the certainty and uncertainty associated with varying post-dinner activities. For example, the probability of falling asleep after dinner is certain (we do this every night). However, the probability of flying to the moon after dinner is impossible (we do not have the equipment to do this). Practice yourself following along with the examples at the end of the video.

An Introduction to Probability

Probability tells us how likely an event is to happen.

We can show probability using numbers from $0$ to $1$. A probability of $0$ means the event is impossible. A probability of $1$ means the event is certain to happen.

Values closer to $0$ describe events that are unlikely. Values closer to $1$ describe events that are likely. A probability of $0.5$, or $\frac12$, means there is an even chance.

For example, a fair coin has an equal chance of landing on heads or tails. Rolling a $7$ on a standard six-sided die is impossible, so its probability is $0$. The probability scale helps us compare events and understand how likely each one is.

Now, that you understand the basics, let's go a little deeper and look at some examples.

Probability is a branch of mathematics that measures how likely a random event is to occur. To find the probability of an event, divide the number of favorable outcomes by the total number of possible outcomes, also called the sample space. This can be written as the ratio of the number of successful outcomes to the total number of outcomes.

For example, when rolling a die, there are six possible outcomes. The chances of rolling an odd number are $\frac{3}{6}$, because there are three odd numbers on a standard die. If you toss a coin, the head and tail are the two possible outcomes, so each has a probability of $\frac{1}{2}$.

Probability can also be used with a deck of cards. The probability of drawing a face card is $\frac{12}{52}$, since there are $12$ face cards in a standard deck.

If a bag contains $3$ red balls and 5 blue balls, the probability of choosing a red ball is $\frac{3}{8}$.

####Look Further

Probability is used in games of chance, science, sports, and everyday decision-making. When an experiment is repeated many times, the number of times an event occurs compared to the total number of trials gives an estimate of its probability. Understanding the outcome of an experiment helps us make predictions about what is likely to happen in the future.

In the next set of lessons, you will continue to learn the fundamentals of probability. We will start with expected value, then learn about the linearity of expectation and compound events.

As we move deeper, we will learn about independent and dependent events and conditional probability.