Students will be able to find theoretical and

ØStudents will be able to find theoretical and experimental probabilities. Algebra 1 Foundations, pg 757

ØStudents 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 rolling an even number Sample Space Favorable Outcomes 1, 2, 3, 4, 5, 6 2, 4, 6 Algebra 1 Foundations, pg 757

ØStudents will be able to find theoretical and experimental probabilities. Focus Question What is the difference between theoretical and experimental probability? ØTheoretical probability is when all possible outcomes are equally likely. ØExperimental probability is based on the results of an experiment. Algebra 1 Foundations, pg 757

ØStudents 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

ØStudents 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 theoretical probability of an even using the following formula. theoretical probability number of favorable outcomes P(event) = number of possible outcomes P(rolling an even #) = P(rolling an odd #) = Algebra 1 Foundations, pg 758

ØStudents 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

ØStudents 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 P(event) = total possible then this is how we find the probability of the complement of an event. what I don’t want P(not event) = total possible Algebra 1 Foundations, pg 759

ØStudents 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 odds in favor of an event = number of unfavorable outcomes Algebra 1 Foundations, pg 759

ØStudents 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 P(event) = # of times the experiment occurs Algebra 1 Foundations, pg 759

ØStudents 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 theoretical probability of rolling a 2? How does the experimental probability of your group compare to theoretical probability?