PROBABILITY bability/basicprobability/preview.we ml

Vocabulary of Probability An outcome is the result of an action. Ex. getting tails is a possible outcome of flipping a coin. An event is a collection of possible outcomes. If all the outcomes are equally likely, you can use a formula to find the theoretical probability.

More about Probability All probabilities range from 0 to 1. Events that cannot happen are impossible events. Events that have a probability of 1 are certain events

Theoretical Probability P(event)= number of favorable outcomes total number of possible outcomes * Probability can be expressed as a fraction, a decimal, or a percent.

Finding Probability Example 1: You select a letter at random from the letters shown. Find the probability of selecting a vowel. Express the probability as a fraction, a decimal, and a percent. A B C D E

Try It On Your Own Find P(consonant) as a fraction for the letters. A B C D E

What is the probability of landing on a number less than 250?

Finding Probabilities from 0 to 1 Example 2: You roll a number cube once. Find the probability of rolling a multiple of 3.

Example 3: Find the probability of rolling a number that is not a multiple of 2.

Try It On Your Own What is the probability of rolling a 9 on a number cube?

Experimental Probability Probability based on experimental data or observations is called experimental probability.

Experimental Probability P(event) = number of times an event occurs total number of trials

Try It On Your Own In 60 coin tosses, 25 are tails. Find the experimental probability.

Sample Space The collection of all possible outcomes in an experiment is the sample space. You can use the sample space to find the probability of an event.

Finding a Sample Space Example 1: Find the probability of rolling at least one 3 on two number cubes. Step 1: Create a table to find the sample space (1,1)(1,1)(2,1)(2,1)(3,1)(3,1)(4,1)(4,1)(5,1)(5,1)(6,1)(6,1) 2(1,2)(1,2)(2,2)(2,2)(3,2)(3,2)(4,2)(4,2)(5,2)(5,2)(6,2)(6,2) 3(1,3)(1,3)(2,3)(2,3)(3,3)(3,3)(4,3)(4,3)(5,3)(5,3)(6,3)(6,3) 4(1,4)(1,4)(2,4)(2,4)(3,4)(3,4)(4,4)(4,4)(5,4)(5,4)(6,4)(6,4) 5(1,5)(1,5)(2,5)(2,5)(3,5)(3,5)(4,5)(4,5)(5,5)(5,5)(6,5)(6,5) 6(1,6)(1,6)(2,6)(2,6)(3,6)(3,6)(4,6)(4,6)(5,6)(5,6)(6,6)(6,6)

Counting Principle The counting principle gives the total number of outcomes. Suppose there are m ways of making one choice and n ways of making a second choice. Then there are m x n ways to make the first choice followed by the second choice. Ex: If you can choose a shirt in 5 sizes and 7 colors, then you can choose among 5 x 7, or 35, shirts.

Try It On Your Own Give the same space for tossing two coins. Find the probability of getting two heads.

Using the Counting Principle Example 2: How many different sandwiches can you order when you choose one bread and one meat from the menu?