Probability

Probability is a measure of how likely something is to happen.

Many events cannot be predicted with certainty, but we can use probability to estimate how likely they are to occur.

Tossing a Coin

When a coin is tossed, there are two possible outcomes: heads (H) or tails (T).

The probability of the coin landing heads is 1/2.

The probability of the coin landing tails is also 1/2.

Throwing Dice

When a single die is thrown, there are six possible outcomes: 1, 2, 3, 4, 5, and 6.

The probability of any one of these outcomes is 1/6.

Probability in General

In general, the probability of an event happening is calculated by dividing the number of ways it can happen by the total number of possible outcomes.

Example:

What is the probability of rolling a 4 on a die?

There is only 1 way to roll a 4, and there are 6 total possible outcomes, so the probability is 1/6.

Another Example:

There are 5 marbles in a bag: 4 are blue and 1 is red. What is the probability of picking a blue marble?

There are 4 ways to pick a blue marble, and there are 5 total possible outcomes, so the probability is 4/5.

Probability Line

We can show probability on a probability line.

The probability line is a number line that ranges from 0 to 1.

The closer a point is to 0, the less likely the event is to happen.

The closer a point is to 1, the more likely the event is to happen.

Words

Some words have special meanings in probability.

• Experiment or Trial: An action where the result is uncertain.
• Sample Space: The set of all possible outcomes of an experiment.
• Sample Point: A single outcome in the sample space.
• Event: A collection of sample points.

Let's use those words so you get used to them:

• Experiment: Flipping a coin is an experiment.
• Sample Space: The sample space for flipping a coin is {heads, tails}.
• Sample Point: A sample point in the sample space for flipping a coin is heads.
• Event: An event in the sample space for flipping a coin is getting heads.

I hope this is helpful!