Math Tech IIII, Jan 16

Transcription

1 Math Tech IIII, Jan 16 Probability IIII Theoretical and Experimental Probability & Compliments Book Sections: 3.1 Essential Questions: What is the difference between probability theory and reality and how does it affect probability? What are complimentary events and what do they have to do with probability? Standards: DA-5.9, DA-5.7, DA-1.5

2 Expected Value To find the number of probable successes over repeated trials, multiply the probability by the number of trials and you will get the likely number of successful trials. This value is called expected value. Expected Value = The probability of the event times number of trials E v = P(event) #Trials

3 Examples If you spin this spinner 100 times, about how many 5 s should result?

4 Examples Using Expected Value.

5 The Basis of Probability Theory To date, every probabilistic model we have considered (dice, coins, spinners, cards, and sequential events) has been based on what should happen if we had true random events and how we would compute probabilities. Probabilities that are based on known characteristics or facts are called theoretical probabilities, and that is what we have studied so far in this unit.

6 Types of Probability Theoretical Probability Probability based on a mathematical model, or what should happen in random events. Experimental Probability - Probability based on repetitions of an actual experiment, computed from the results of a lot of observations, or what actually happens in random events.

7 Theory Can Only Cover so Many Bases If we have complete knowledge of the set of possible outcomes of an event, then theoretical probability is a good predictor of what should happen. If we don t know how an experiment will behave or the outcome of event will occur, there is no way of predicting results based on theories, so we have to gain that knowledge by conducting the experiment many times.

8 Experimental Probability What it Means Experimental probability is a probability based on conducting an experiment over and over and can vary as the experiment is continually repeated.

9 Computing Experimental Probability Experimental probability is computed from manymany actual observations P(event) = Number of favorable outcomes observed Total number of Trials

10 An Example Over the last eight years, Farmer Jones has determined that only five out of six corn seeds planted on his 3000 acre farm produce corn. Is this theoretical or experimental probability? Experimental because it is based on what happened in the past. If Farmer Jones wants 10,000 corn-bearing plants, how many should he plant?

11 An Example Over the last eight years, Farmer Jones has determined that only five out of six corn seeds planted on his 3000 acre farm produce corn. Is this theoretical or experimental probability? Experimental because it is based on what happened in the past. If Farmer Jones wants 10,000 corn-bearing plants, how many should he plant?

12 Example Two Quality control at a fan belt factory randomly selects 200 production belts a day and tests their quality. Over a ten day period, they have found a total of 15 defective fan belts. Experimental because it is based on sampling and testing (experimenting). What is the experimental probability that any given fan belt is defective from this factory?

13 Example Two, Answer What is the experimental probability that any given fan belt is defective from this factory?

14 Examples

15 Complementary Events An event will either happen or it will not. All possible outcomes that are not an event add up to be the compliment of that event. The sum of the probability of an event and the event s compliment always add up to 1 or P(event) + P(not the event) = 1, where P(not the event) is the probability of the event s compliment.

16 The Probability of Complimentary Events P(event) = 1 P(event will not occur) In words: The probability of an event happening is 1 the probability it will not happen.

17 Examples

18 Examples

19 Class work: CW 1/11, 1-21 Homework: None