 Students will be able to find theoretical and experimental probabilities.

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.  Students will be able to find theoretical and experimental probabilities. Here is how these terms apply to rolling an even number on a number cube: EventSample SpaceFavorable Outcomes rolling an even number 1, 2, 3, 4, 5, 6 2, 4, 6

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

Algebra 1 Foundations, pg 757 The probability of an event, or P(event), tells you how likely it is that the event will occur  Students will be able to find theoretical and experimental probabilities. 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 758 When all possible outcomes are equally likely, you can find the theoretical probability of an even using the following formula.  Students will be able to find theoretical and experimental probabilities. theoretical probability P(event) = number of favorable outcomes number of possible outcomes P(rolling an even #) = P(rolling an odd #) =

Theoretical vs. Experimental Probability Example 1: Roll a dice. What is the theoretical probability of rolling a 4? # favorable outcomes # possible outcomes 1 6 The probability of rolling a 4 is 1 out of 6

Algebra 1 Foundations, pg 758 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.  Students will be able to find theoretical and experimental probabilities. P(event) + P(not event) = 1

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

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

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

Theoretical vs. Experimental Probability Example 1 Continued: Roll a dice. What is the experimental probability of rolling a 4? # event occurrences Total # of trials

Experimental: You tossed a coin 10 times and recorded a head 3 times, a tail 7 times P(head)= 3/10 P(tail) = 7/10 Theoretical: Toss a coin and getting a head or a tail is 1/2. P(head) = 1/2 P(tail) = 1/2

Identifying the Type of Probability A bag contains three red marbles and three blue marbles. P(red) = 3/6 =1/2 Theoretical (The result is based on the possible outcomes)

Identifying the Type of Probability You draw a marble out of the bag, record the color, and replace the marble. After 6 draws, you record 2 red marbles P(red)= 2/6 = 1/3 Experimental (The result is found by repeating an experiment.)

Algebra 1 Foundations, pg 761  Students will be able to find theoretical and experimental probabilities.

Algebra 1 Foundations, pg 762  Students will be able to find theoretical and experimental probabilities.

Algebra 1 Foundations, pg 762  Students will be able to find theoretical and experimental probabilities.

Algebra 1 Foundations, pg 762  Students will be able to find theoretical and experimental probabilities.