Objective We will learn the characteristics of Bernoulli trials and how to calculate probabilities based on geometric models Get out paper for notes Closing task I will complete and exit ticket in which I calculate the geometric probabilities of four events ID: 1045817
Download Presentation The PPT/PDF document "Ch 17 – Probability Models" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
1. Ch 17 – Probability ModelsObjectiveWe will learn the characteristics of Bernoulli trials and how to calculate probabilities based on geometric modelsGet out paper for notesClosing taskI will complete and exit ticket in which I calculate the geometric probabilities of four events.HomeworkPg 398 – 399 # 2, 8, 10, 12 Warm-up
2. Chapter 17Probability Models
3. Only two possible outcomes (success or failure)Independent from trial to trialFixed probability of success for each trial.EX) Flipping a coin, guessing on a True or False Test, throwing a die for a certain number.Bernoulli Trial Characteristics
4. Does it make sense? Is there any reason why one trial would affect the other? ….. If not assume independence.10% Conditionusually violated when we sample without replacementIf you don’t drain off more than 10% of population, we assume independence.Proving Independence
5. Pulling 3 hearts from a deck of cards?Picking 3 male students at random from the class?Picking 100 people with Type AB blood from the population?10% Condition Example
6. We roll 50 dice to find the distribution of the number of spots on the faces?Are there only two outcomes?Is the probability of success the same for each observation?Is each event independent?Bernoulli or Not?
7. How likely is it that in a group of 120, the majority may have Type A blood, given that Type A is found in 43% of the population?Are there only two outcomes?Is the probability of success the same for each observation?Is each event independent?Bernoulli or Not?
8. We deal 5 cards from a deck and get all hearts. How likely is that?We wish to predict the outcome of a vote on the school budget, and poll 500 of the 3000 likely voters to see how may favor the proposed budget.A company realizes that about 10% of its packages are not being sealed properly. In a case of 24, is it likely that more than 3 are unsealed?Bernoulli or Not?
9. Must obey Bernoulli characteristics to use.Use when you are counting the number of trials to required to achieve first success.Geometric Probability
10. P(X=x) = q(x-1)pp = probability of successq = (1 – p) or probability of failurex = # of trials until first success occursGeometric Probability
11. µ = µ = the expected value (the average # of trials it will take to achieve our first success) Geometric Probability
12. People with O-negative blood are called “universal donors”. Only about 6% of people have O-negative blood. If donors line up at random for a blood drive how many do you expect to examine before you find someone with O-negative blood?Is this a Bernoulli Trial?Type O Blood Donors
13. People with O-negative blood are called “universal donors”. Only about 6% of people have O-negative blood. What is the probability that the first O-negative donor is the 2nd person in line?Type O Blood Donors
14. People with O-negative blood are called “universal donors”. Only about 6% of people have O-negative blood. What is the probability that the first O-negative donor is the 5th person in line?Type O Blood Donors
15. P(X≤ x) = P(x=1) + P(x=2) + …P(x=x)Used for finding the success within a certain number of trialsGeometric Probability
16. People with O-negative blood are called “universal donors”. Only about 6% of people have O-negative blood. What is the probability that the first O-negative donor is found in one of the first 5 people?Type O Blood Donors
17. 2nd DISTR geometpdf(p,x)Probability density functionUsed to find the first success in exactly the xth trial.p = probability of success ( what you are looking for)2nd DISTR geometcdf(p,x)Probability cumulative functionUsed to find the probability on or before a certain xth trial.These could also be calculated with “at least” formulaCalculator Tips
18. Ex. The probability of being left handed is 13%. What is the probability that the 3rd person I sample is the first Left-hander?Geometpdf(.13,3)What is the probability that I don’t run into a right-hander until the 5th person?Geometpdf(.87,5) Examples
19. Ex. The probability of being left handed is 13%. What is the probability that there are some lefties in the first five people?Geometcdf(.13,5)What is the probability that I get a righty within the first three people?Geometpdf(.87,3) Example
20. A basketball player has made 80% of his foul shots during the season. Assuming the shots are independent, find the probability that in tonight’s game he…Misses for the first time on his fifth attempt.Makes his first basket on his fourth shot.Makes his first basket on one of his first 3 shots.What is the expected number of shots until he makes it?What is the expected number of shots until he misses?Hoops
21. Ch 17 – Probability ModelsObjectiveWe will learn the characteristics of Bernoulli trials and how to calculate probabilities based on geometric modelsClosing taskI will complete and exit ticket in which I calculate the geometric probabilities of four events.HomeworkPg 398 – 399 # 2, 8, 10, 12