Unit 12. Applications of Probability

12.1: What Is Probability?

Definitions: Probability

In Probability, we are talking about the likelihood that some event will occur.

The probably of some event is written as ... and runs from 0% (the event will never happen) to 100% (the event will always happen). It may be written as decimals, from 0 to 1, or as fractions. A probability will never be negative or more than 1.

The set of ways something can happen is the sample space.

The event we're interested in are the outcome.

Definitions: Probability

If we are flipping a coin and we've called Heads, the sample space is {Heads,Tails} and the outcome is {Heads}.

If we are rolling a six-sided die and we're looking to get a number more than 2, the sample space is {1,2,3,4,5,6} and the outcome is {3,4,5,6}.

Calculating Simple Probability

If all outcomes are equally likely, you can calculate the probability of an event occurring using:

...

Calculating Simple Probability

What is the probability of flipping a coin and getting heads?

As above, the sample space is {Heads,Tails}, which has 2 elements, and the outcome is {Heads}, which has 1.

So the probability of getting heads is ...

What is the probability of rolling a 6-sided die and getting a number more than 4?

The sample space for rolling a 6-sided die is {1, 2, 3, 4, 5, 6}, which has 6 elements.

The outcomes we're interested in, the numbers more than 4, are {5, 6}, which has 2 elements.

So the probability of rolling a number more than 4 is ...

What is the probability of flipping a coin twice and getting heads both times?
What are the possible ways we can flip a coin twice? {HH, HT, TH, TT} has 4 elements. There is only one way to get heads both time: {HH} has 1 element.

So the probability of getting heads twice is ...