University:
Missouri State University
Course:
MTH 343 | Foundations of Probability and Statistics for Teachers
Academic year:

2020
Views:

453

Pages:

3
Author:

Nico Bryan

Gn. 17: Probability Models (Geometric vs. Binomiall Opening question have a game in which you spin a spinner for your prize. The spinner has 4 sections: Red 45%, Green 30%. 15%. You win if you spin RED Answer the following questione P(R) = 0.45 1-2- What is the probability of wirming for the first time on the 10 spin? (R^ 2 cap R^ 2 cap R)= 0.19612 * 0.5 ^ 2 * (0.55) ^ 2 * (0.55) ^ 2 * (0.45) P(RINRARAR) = 0.002 (055) (0.45) the probability that it will take you 18 sins before you get your first blue? P(s) = 0.15 P(BinBin BinB)=0.0095 How can I simplify my process for any of the above questions? (0.05) (015 (1 - p) ^ (n - 1) * (p)' p This type of question is a specific type of probability, and hag aapeel NOTATION: GED GEOMETRIC MODELS Continue fra ves There are 4 conditions that must apply to the trials 2 possible outcomes Probability of success is constant called pr Number of triat UNKNOZIN Independent tru 10% Condition: if we cannot assume independence, we can proceed as long as the sample is smaller than 10% of the population (pop 10) For GEOMETRIC MODELS P(X-k)-p Expected value: EDX) P Standard deviationc 5000 typo VOCAB Bernoulli trial There are two outcomes (success/fallure) The probability of success is constant Independent trials (or 10% condition) VOCAB: Geometric models Above 3 conditions and... Bernavilli Geom Binom Models in which we continue UNTIL we get a success VOCAB Binomial models Above 3 conditions and Models in which we have a SEI number of trials, and we are asking questions about a certain number of successes. Example: Suppose a computer chip manufacturer consistently rejects 2% of the chips produced because they fail presale testing. a) Is this a Bernoulli tal • reject 0.0% not rejected 0.98 •p=0.02+ constant 0 * 10 = 5 * 10 = 50thea are more than computer chips made bị What is the probability that the 5" cho you test is the first bad one you find? G(0.02) P(x-s) (0.18) (0.02)-6.018 What is the probability that you find your first bad one within the first 4 you examine? 6(0.03) (0) P( P(x + 1) f' * (x = 3) gem adf B(4,0.02) P(x >= 1) chip? What is the standard deviation? 6(098) } add up What is the expected of chips you need to check until you find a good sigma_{x} = (sqrt(p))/p = (sqrt(1 - p))/p P( leftarrow n6n < n < n8) \mathcal{D}_{6x} = 1/0.88 =1.03.chi rho s tilde O_{x} = (sqrt(8pi))/0.98 =0.1443 ehigs