P - Theoretical Probability Lesson

Theoretical Probability

In this lesson, you will learn to find the theoretical probability of an event. Theoretical probability is used to find the probability of an event when all the outcomes are equally likely. The theoretical probability of an event is the ratio of the number of ways the event can occur to the number of possible outcomes.

equation image indicator $LaTeX: Probability\:=\frac{\:number\:of\:ways\:the\:event\:can\:occur}{total\:number\:of\:equally\:likely\:outcomes}$ $Probability\:=\frac{\:number\:of\:ways\:the\:event\:can\:occur}{total\:number\:of\:equally\:likely\:outcomes}$

Example

image of deck of cards text annotation indicator Shelby is going to select a random card from a stack of 14 cards. They are numbered from 1 to 14. What is the probability that she chose a card with a number less than 6?

1. Count the number of favorable outcomes. There are 5 cards less than 6 (1, 2, 3, 4, and 5)

2. Count the number of possible outcomes. There are a total of 14 cards, each with the same chance of being drawn

3. Find the theoretical probability.

4. equation image indicator $LaTeX: P\left(card\:with\:number\:less\:than\:6\right)=\frac{\:number\:of\:ways\:the\:event\:can\:occur}{total\:number\:of\:equally\:likely\:outcomes}=\frac{5}{14}$ $P\left(card\:with\:number\:less\:than\:6\right)=\frac{\:number\:of\:ways\:the\:event\:can\:occur}{total\:number\:of\:equally\:likely\:outcomes}=\frac{5}{14}$

5. The probability of selecting a card less than 6 is equation image indicator $LaTeX: \frac{5}{14}$ $\frac{5}{14}$ and is unlikely.

Example

image of bag of marbles text annotation indicator Andy has 25 marbles in a bag. Of these, 10 are clear and 15 are blue. Find the probability of drawing a clear marble from the bag? Write your answer as a fraction, as a decimal, and as a percent.

1. equation image indicator $LaTeX: Probability\:=\frac{\:number\:of\:ways\:the\:event\:can\:occur}{total\:number\:of\:equally\:likely\:outcomes}$ $Probability\:=\frac{\:number\:of\:ways\:the\:event\:can\:occur}{total\:number\:of\:equally\:likely\:outcomes}$

2. equation image indicator $LaTeX: P\left(clear\right)=\frac{number\:of\:clear\:marbles}{total\:number\:of\:marbles}=\frac{10}{25}=\frac{2}{5}=0.40,\:40\%$ $P\left(clear\right)=\frac{number\:of\:clear\:marbles}{total\:number\:of\:marbles}=\frac{10}{25}=\frac{2}{5}=0.40,\:40\%$

3. The theoretical probability of drawing a clear marble is equation image indicator $LaTeX: \frac{2}{5},\:or\:0.40,\:or\:40\%$ $\frac{2}{5},\:or\:0.40,\:or\:40\%$

We have learned that Theoretical probability is what we expect to happen when all outcomes are equally likely, whereas Experimental probability is what really happens when we actually do the experiment. We calculate probability the same and the more trials we conduct, the closer experimental probability gets to theoretical probability.

Watch this video to see examples and comparisons of experimental and theoretical probability.

Now see how well you understand the terms involved in Theoretical Probability.

Theoretical Probability Practice

Match the word that fills in the blank.

Theoretical Probability Homework

Now that you have spent some time learning strategies for solving problems involving theoretical probability, you are ready to complete your Probability: Theoretical Probability Homework. Download your homework by CLICKING HERE. Links to an external site.

Once you have completed your homework, AND MAKE SURE YOU ATTEMPTED AND WORKED THE PROBLEMS OUT ON YOUR OWN, click here to download your homework key. Links to an external site.

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