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Introduction to Probability

The Measure of Chance

Probability is a way to measure how likely it is for something to happen. It's a number between 0 and 1. If an event has a probability of 0, it's impossible. If it has a probability of 1, it's certain to happen.

A probability of 0.5 means an event has a 50/50 chance, like a fair coin landing on heads.

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Sample Spaces and Events

To calculate probability, we first need to know all the possible results of an action. This complete set of outcomes is called the sample space.

For a single coin toss, the sample space is {Heads, Tails}. For a standard six-sided die roll, the sample space is {1, 2, 3, 4, 5, 6}.

An event is the specific outcome or group of outcomes you're interested in. It's a subset of the sample space. For example, if you're rolling a die, an event could be "rolling a 4" or "rolling an odd number."

Calculating Simple Probability

Once you know the sample space and the event, calculating probability is straightforward. You just need to count.

P(Event)=Number of favorable outcomesTotal number of possible outcomesP(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}

Let's use our dice example. What's the probability of rolling an even number?

The sample space is {1, 2, 3, 4, 5, 6}, so there are 6 total possible outcomes. The event (rolling an even number) includes the outcomes {2, 4, 6}, which is 3 favorable outcomes.

P(Even)=36=12=0.5P(\text{Even}) = \frac{3}{6} = \frac{1}{2} = 0.5

This means you have a 50% chance of rolling an even number on a standard die.

Quiz Questions 1/5

If the probability of an event is 1, what does this signify?

Quiz Questions 2/5

What is the sample space for flipping a single, standard coin?