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Introduction to Statistics: Help and Review9 chapters | 137 lessons

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Lesson Transcript

Instructor:
*Lance Cain*

Have you ever heard someone ask, 'What are the odds?' Usually what it is meant is, 'How likely is it that an event will happen?' This lesson explores finding the likelihood, or theoretical probability, that an event could occur.

The very first Super Bowl was played at Anaheim Stadium in Los Angeles in 1967. It was a battle between the Green Bay Packers and the Kansas City Chiefs. This historical game started the same way all football games begin, with a coin toss. If you were standing on the 50-yard line as one of the team captains, what are the odds that you would win the coin toss? If you said 50% you were right. Here's how it's calculatedâ€¦

A normal coin has two sides, *heads* and *tails*. So, when you flip a coin, there are two, and only two, possible outcomes; the coin either lands with the head side up or it lands with the tails side up. So, the total number of possible outcomes for a coin flip is 2, and it is equally likely for the coin to land on either side. This means the probability of getting heads (or tails) on a single flip of the coin is 1 out of 2, or 50%.

But what if the odds are not as even as 50/50? Well, let's suppose there were a gumball machine filled with red, green, yellow, orange and blue gumballs, and you only had one quarter to get a red one. In order to calculate the probability, you need to know two things: (a) the total number of gumballs in the machine, and (b) the number of red ones.

The total number of gumballs represents the total possible outcomes, supposing that you are equally likely to pick any one of them. And the number of red gumballs represents the number of possible favorable outcomes (outcomes you are interested in). So, the **theoretical probability** is equal to the number of favorable outcomes (in this case the number of red gumballs) divided by the total number of possible outcomes (in this case the total number of gumballs in the machine).

**Example A:**

There are 5 red balls, 7 green balls and 13 blue balls in the bag.

- The theoretical probability of picking a red ball is 5 divided by 25, which is 1/5 or 20%
- The theoretical probability of picking a green ball is 7 divided by 25, which is 7/25 or 28%
- The theoretical probability of picking a blue ball is 13 divided by 25, which is 13/25 or 52%

**Example B:**

What is the theoretical probability that a monkey in the elevator of a 20-story hotel will randomly press the right button to get you to your floor? Well, assuming you only have one room at the hotel, then there is only 1 right button out of 20 possible buttons the monkey could select. Therefore, the theoretical probability is 1 out of 20, which is 1/20 or 5%.

**Theoretical probability** is a method to express the likelihood that something will occur. It is calculated by dividing the number of favorable outcomes by the total possible outcomes. The result is a ratio that can be expressed as a fraction (like 2/5), or a decimal (like .40), or most commonly as a percentage (like 40%).

Theoretical probability is:

- A way to express how likely something is to happen
- Calculated by dividing the number of preferred outcomes by the number of possible outcomes
- Usually expressed as a fraction of percentage

Once you've finished, practice what you learned:

- Explain what theoretical probability is
- Recall the equation for theoretical probability
- Calculate the theoretical probability of an outcome

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Introduction to Statistics: Help and Review9 chapters | 137 lessons

- Mathematical Sets: Elements, Intersections & Unions 3:02
- Events as Subsets of a Sample Space: Definition & Example 4:51
- Probability of Simple, Compound and Complementary Events 6:55
- Probability of Independent and Dependent Events 12:06
- Probability of Independent Events: The 'At Least One' Rule 5:27
- How to Calculate Simple Conditional Probabilities 5:10
- The Relationship Between Conditional Probabilities & Independence 7:52
- Using Two-Way Tables to Evaluate Independence 8:09
- Applying Conditional Probability & Independence to Real Life Situations 12:32
- The Addition Rule of Probability: Definition & Examples 10:57
- The Multiplication Rule of Probability: Definition & Examples 8:37
- Math Combinations: Formula and Example Problems 7:14
- How to Calculate a Permutation 6:58
- How to Calculate the Probability of Permutations 10:06
- Relative Frequency & Classical Approaches to Probability 5:56
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