Section 4 – 5 Applying Ratios to Probability Objectives: To find theoretical probability To find experimental probability

Probability of an Event: P(event) Tells you how likely it is that something will occur Event: Any outcome or group of outcomes Outcome: The result of a single trial, like one roll of a number cube Same Space: All of the possible outcomes

Example: P(rolling an even number) Event: Rolling an even number on a number cube. Sample Space (possible outcomes): 1, 2, 3, 4, 5, 6 Favorable Outcome: 2, 4, 6

When all possible outcomes are equally likely to occur, you can find the theoretical probability using the following formula:

The probability of an event can be written as a fraction, decimal or percent.

Example 1 Finding Theoretical Probability A)What is the probability of flipping a coin and getting a tail. B)What is the probability of rolling a 1 or 6 on a die?

C)What is the probability of spinning purple? D)What is the probability of spinning white or green?

E)A bowl contains 12 slips of paper, each with a different name of a month. Find the theoretical probability that a slip selected from the bowl has a name of a month that starts with the letter J. F)Suppose you write the names of days of the week on identical pieces of paper. Find the theoretical probability of picking a piece of paper at random that has the name of a day that starts with the letter T.

Complement of an event: All of the outcomes NOT in the event. The probability of an event and its complement add up to 1!

C)What is the probability of spinning purple? D)What is the probability of spinning white or green? D)What is the probability of NOT spinning purple?

Example 2 Finding the Complement of an Event A) Find the probability of NOT flipping a coin and getting a tail. B)What is the probability of NOT rolling a 1 or 6 on a die?

C)On a popular television game show, a contestant must choose one of five envelopes. One envelope contains the grand prize, a car. Find the probability of NOT choosing the car. D)You decide to buy 50/50 tickets at the football game on Saturday. If 50 people buy 10 tickets each, what is the probability that they will not pick your ticket? What happens to the P(not picking your ticket) if the number of tickets bought increases?

Experimental Probability: Probability based on data collected from repeated trials.

How Does Experimental Probability & Theoretical Probability Compare? The more times an experiment is done, the closer the experimental probability gets to the theoretical probability. We call this the Law of Large Numbers.

A)After receiving complaints, a skateboard manufacturer inspected 1000 skateboarders at random. The manufacturer found no defects in 992 skateboards. What is the probability that a skateboard selected at random had no defect? Example 3 Finding Experimental Probability

B)The skateboard manufacturer decides to inspect 2500 skateboards. There are 2450 skateboards that have no defects. Find the probability that a skateboard selected at random has no defects.

Example 4 Using Experimental Probability A)A manufacturer has 8976 skateboards in its warehouse. If the probability that a skateboard has no defect is 99.2%, predict how many skateboards are likely to have no defect.

B) A manufacturer has 8976 skateboards in its warehouse. If the probability that a skateboard has no defect is 81%, predict how many skateboards are likely to have defects.