# Andy Sandbox

A **probability** is a number that represents the likelihood of an uncertain event. Probabilities are always between 0 and 1, inclusive. The larger the probability, the more likely the event is to happen. A probability of 0 means that the event is impossible; it will never happen. A probability of 1 means that the event is assured; it will always happen. All other values between 0 and 1 represent various levels of likelihood.

The study of probability is important because it deals with quantifying problems with uncertain results. For example, in manufacturing, it is never certain that every product that you produce is perfect. It would be incredibly costly and excessive to have a Quality Assurance team meticulously test every single product that goes out the door. Understanding the probability of a defect, however, allows a manufacturing company to handle defects much more intelligently.

## Games of Chance

One of the easiest ways to start understanding probability is to study games of chance.

What is the probability of rolling three 6s when rolling three fair six-faced dice?

The probability of rolling a 6 on each die is \(\frac{1}{6}.\) Then the probability of rolling three 6s is \(\frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} = \frac{1}{216}.\)

Some kind of integrated link/advertisement for Games of Chance course? Or would that be too on-the-nose?

## Practical Applications

As you begin to gain a greater understanding of probability, you can use it in practical applications. Some applications include sports, economics, science, and manufacturing.

99% effective vaccine example

I booked center court tickets for the Wimbledon Men's Final best-of-five match. As luck would have it, I got stuck in traffic and now I cannot make it to the court before the match starts. However, I will certainly be able to make it just before the start of the fifth set (if there is one).

If each player has a 50% chance of winning each set, what is the probability that I would miss the match completely (with no fifth set played)?

Just like above, do we include an integrated link/advertisement to Probability course?