 Ch 17 – Probability Models 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. Homework Pg 398 – 399 # 2, 8, 10, 12 Warm-up

Probability Models

 1)Only two possible outcomes (success or failure) 2)Independent from trial to trial 3)Fixed 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

  Does it make sense?  Is there any reason why one trial would affect the other? ….. If not assume independence.  10% Condition  usually violated when we sample without replacement  If you don’t drain off more than 10% of population, we assume independence. Proving Independence

  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

  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?

  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?

  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?

  Must obey Bernoulli characteristics to use.  Use when you are counting the number of trials to required to achieve first success. Geometric Probability

 P(X=x) = q (x-1) p p = probability of success q = (1 – p) or probability of failure x = # of trials until first success occurs Geometric Probability

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  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

  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 2 nd person in line? Type O Blood Donors

  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

 P(X≤ x) = P(x=1) + P(x=2) + …P(x=x) Used for finding the success within a certain number of trials Geometric Probability

  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

  2 nd DISTR geometpdf(p,x)  Probability density function  Used to find the first success in exactly the xth trial.  p = probability of success ( what you are looking for)  2 nd DISTR geomet c df(p,x)  Probability cumulative function  Used to find the probability on or before a certain xth trial. Calculator Tips

  Ex. The probability of being left handed is 13%. What is the probability that the 3 rd 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 5 th person?  Geometpdf(.87,5) Examples

  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

  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

 Ch 17 – Probability Models Objective  We will learn the characteristics of Bernoulli trials and how to calculate probabilities based on geometric models Closing task  I will complete and exit ticket in which I calculate the geometric probabilities of four events. Homework Pg 398 – 399 # 2, 8, 10, 12