Probability

Ever wondered if it will rain tomorrow or if you will win a game? That’s probability! It is a mathematical way to measure how likely an event is to happen.

An outcome is one possible result of a random experiment.

All possible outcomes are the complete list of all the outcomes that can happen in a random experiment.

What are all the possible outcomes when you flip a coin?

What are all the possible outcomes when you roll a six-sided die?

An event is a set of outcomes from the set of all possible outcomes.

In the experiment of rolling a die, find the outcomes that correspond to rolling an even number.

We use special words to describe the chance of an event happening. We can place these words on a line from least likely to most likely.

• Impossible: It can’t happen.
  Example: Riding a dinosaur.
• Less likely: It probably won’t happen.
  Example: Rolling a die and getting a 3.
• Even chance: It has the same chance to happen or not to happen.
  Example: Tossing a coin and getting heads.
• More likely: It will probably happen.
  Example: Drinking water at school today.
• Certain: It will happen.
  Example: The sun will rise tomorrow.

When you flip a coin, there are two possible outcomes: heads or tails. The chance of getting heads is 1 out of 2. We can write this as a fraction:

The probability of an event, written \(P(\text{event})\), is a number from 0 (impossible) to 1 (certain).

In many experiments, each outcome has the same chance of happening. For example, a fair coin is just as likely to land on heads as it is on tails. When we roll a fair die, each number from 1 to 6 has the same chance of appearing. We call these equally likely outcomes.

When all outcomes of an experiment are equally likely, we can calculate the probability of an event using a simple formula:$$P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$“Favorable outcomes” are the outcomes that match the event we are interested in.

A fair six-sided die is rolled. Calculate the probability of rolling an even number.