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Probability Models

Probability Models. The Bernoulli Family. The Bernoulli Family. What is a Bernoulli trial? Q1: do not use wikipedia !. 3 characteristics: two possibilities (yes/no, true/false, success/failure) constant probability of success

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Probability Models

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  1. Probability Models The Bernoulli Family

  2. The Bernoulli Family

  3. What is a Bernoulli trial?Q1:do not use wikipedia! 3 characteristics: two possibilities (yes/no, true/false, success/failure) constant probability of success all events are independent or your sample is less than 10% of the population

  4. Give 2 examples of a Bernoulli trial?Q2: 2 examples 3 characteristics: two possibilities (yes/no, true/false, success/failure) constant probability of success all events are independent

  5. Two types of Bernoulli trials.Q3:give an example of each! Geometric: applies to waiting time situations – counting the number of trials to achieve our first success. How many components until the first success? Binomial: count the number of successes we get in a given number of trials. P(4 successes given 10 trials)

  6. Skittles!Q4:is this a Bernoulli trial? Check the assumptions. The manufacturer says that there are 20% of the red ones that I like best. I jiggle my machine and one slips out. • Two outcomes: red or other • Probability of red is 20% • Getting one candy does not effect the next candy.

  7. Skittles!Q5:is this a geometric or binomial? What is the probability that the first red candy is the 4th candy selected? They are consecutive, one after the other so we are multiplying . P(red c) P(red c) P(red c) P(red) • (0.8)(0.8)(0.8)(0.2) = ? • Or • P(1st red is the nth) = qn-1p • Where q is the P(failure)

  8. Skittles! What is the probability that the first red candy is the 4th candy selected? • This is a Geometric Probability Model • Looking for the FIRST success of a Bernoulli trial • Find the expected value of getting a red skittle; on average, how many do you need to select to get a red one? Create a probability model.

  9. Skittles! Q6 & Q7:what is the formula for the mean and stdev of a Geom(p) model What is the probability that the first red candy is the 4th candy selected? • Find the stdev of the model Geom(p) • And the stdev

  10. Skittles! Q8:is this a geometric or binomial? What is the probability that the first red candy is one of the first 3 that comes out? {could be the 1stor 2nd or 3rd } We are adding probabilities here. P(1st) + P(2nd) + P(3rd ) • (0.8)0(0.2)+(0.8)1(0.2)+(0.8)2(0.2) = ?

  11. Skittles!Q9:how many different ways can you get 1 red out of 3 total? .2 What is the probability that out of 3 candies, one will be red? .2 .2 .8 .8 .8

  12. Skittles! What is the probability that out of 3 candies, one will be red? 3 x P(1 red) • 3 x (0.8)2(0.2)= ?

  13. Skittles! What is the probability that out of 3 candies, one will be red? • This is a Binom(n, p) model • Its mean or E(X) = np • Its stdev or  = npq

  14. Skittles 3 Q10:is this a geometric or binomial? What is the probability that out of 12 candies, four will be red? {just try to do a tree out of this one! I dare you}

  15. Combinations: when the order doesn’t matter, just how many ways it can occur. Q11:how many ways can you get 4 reds out of 12 skittles

  16. Skittles 3 Q12a-e:identify n, r, p, q, and n-r What is the probability that out of 12 candies, four will be red?

  17. The Bernoulli Family

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