Theoretical and Experimental Probability Ch 12-7 Students will be able to find theoretical and experimental probabilities. Theoretical and Experimental Probability Algebra 1 Foundations, pg 757

Ch 12-7 Students will be able to find theoretical and experimental probabilities. In the Solve It, spinning red and choosing the right envelop are the desired outcomes. An outcome is the result of a single trial, such as spinning a wheel. The sample space is all possible outcomes. An event is any outcome or group of outcomes. The outcomes that match a given event are favorable outcomes. Here is how these terms apply to rolling an even number on a number cube: Event Sample Space Favorable Outcomes rolling an even number 1, 2, 3, 4, 5, 6 2, 4, 6 Algebra 1 Foundations, pg 757

Ch 12-7 Students will be able to find theoretical and experimental probabilities. Focus Question What is the difference between theoretical and experimental probability? Theoretical probability is when all possible outcomes are equally likely. Experimental probability is based on the results of an experiment. Algebra 1 Foundations, pg 757

Ch 12-7 Students will be able to find theoretical and experimental probabilities. The probability of an event, or P(event), tells you how likely it is that the event will occur. You can find probabilities by reasoning mathematically or by using data collected from an experiment. You can write the probability of an event as a fraction, a decimal, or a percent. The probability of an event ranges from 0 to 1. Algebra 1 Foundations, pg 757

theoretical probability Ch 12-7 Students will be able to find theoretical and experimental probabilities. In the number-cube example, the outcomes in the sample space are equally likely to occur. When all possible outcomes are equally likely, you can find the theoretical probability of an even using the following formula. theoretical probability number of favorable outcomes number of possible outcomes P(event) = P(rolling an even #) = P(rolling an odd #) = Algebra 1 Foundations, pg 758

Ch 12-7 Students will be able to find theoretical and experimental probabilities. The complement of an event consists of all outcomes in the sample space that are not in the event. The sum of the probabilities of an event and its complement is 1. P(event) + P(not event) = 1 The possible outcomes for rolling a number cube are 1 2, 3, 4, 5, and 6. The outcomes for rolling an even number are 2, 4, and 6. The outcomes for the complement of rolling an even number are 1, 3, and 5, all the odd numbers. P(evens) + P(not evens) = 1 Algebra 1 Foundations, pg 758

Ch 12-7 How do we find the probability of the complement of an event? Students will be able to find theoretical and experimental probabilities. How do we find the probability of the complement of an event? If this is how we find the probability of an event, what I want total possible P(event) = then this is how we find the probability of the complement of an event. what I don’t want total possible P(not event) = Algebra 1 Foundations, pg 759

number of favorable outcomes number of unfavorable outcomes Ch 12-7 Students will be able to find theoretical and experimental probabilities. Odds describe the likelihood of an event as a ratio comparing the number of favorable and unfavorable outcomes. number of favorable outcomes number of unfavorable outcomes odds in favor of an event = Algebra 1 Foundations, pg 759

experimental probability Ch 12-7 Students will be able to find theoretical and experimental probabilities. Experimental probability is based on data collected from repeated trials. experimental probability # of times an event occurs # of times the experiment occurs P(event) = Algebra 1 Foundations, pg 759

Ch 12-7 Students will be able to find theoretical and experimental probabilities. With your group, find the experimental probability of rolling a 2. Group 1: P(2) = Group 3: P(2) = Group 2: P(2) = Group 4: P(2) = What is the theoretical probability of rolling a 2? How does the experimental probability of your group compare to the theoretical probability?

Ch 12-7 Students will be able to find theoretical and experimental probabilities. Algebra 1 Foundations, pg 761

Ch 12-7 Students will be able to find theoretical and experimental probabilities. Algebra 1 Foundations, pg 761

Ch 12-7 Students will be able to find theoretical and experimental probabilities. Algebra 1 Foundations, pg 762

Ch 12-7 Students will be able to find theoretical and experimental probabilities. Algebra 1 Foundations, pg 762

Ch 12-7 Students will be able to find theoretical and experimental probabilities. Algebra 1 Foundations, pg 762