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# SMC MATH 21 - Finite Math section 8.6 Bernoulli Experiment and Binomial Distribution

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Finite Mathsection 8.6 Bernoulli Experiment and Binomial Distribution. Bernoulli experiment is an activity of n repeated trials where each trial has 2 possible outcomes and each trial is independent.Ex1, A coin is tossed 3 times. Outcome of each coin toss is H or T. (a) Find the sample space. (b) Construct probability distribution chart. (order of outcome is respected.) (c) Construct binomial distribution chart. (order of outcome is ignored)Formulas on probablity of Bernoulli experiments. (Binomial distribution) Let there be n repeated trials of an experiment where p = probability of success in each trial and q = 1 p = probability of failure in each trial. Let x = # of successes in n trials. then P(x = k) = C(n, k) p q .knkEx2, A coin is tossed 5 times. Let Success be a H. Therefore, p = and q = 1122 (a) P(x = 0) (b) P(x = 1) (c) P(x = 2) (d) P(x = 3) (e) P(x = 4) (f) P(x = 5) (g) Construct binomial distribution chart. (order of outcome is ignored)Ex3, A die is rolled is rolled 3 times. Let Success be a 1 or 2. Therefore, p = and q = 1233 (a) P(x = 0) (b) P(x = 1) (c) P(x = 2) (d) P(x = 3) (e) Construct binomial distribution chart. (order of outcome is ignored)Ex4, A die is rolled is rolled 4 times. Let Success be a 6. Therefore, p = and q = (a) P(x = 0) (b) P(x = 1) (c) P(x = 2) (d) P(x = 3) (e) P(x = 4) (f) Construct binomial distribution chart. (order of outcome is ignored)Ex5, Let each trial be the event where1 card is drawn from a standard deck of 52 cards, then the card is put back into the deck. Let there be 5 trials. For each trial, let Success be the event where a Diamond is drawn. (a) P(x = 0) (b) P(x = 1) (c) P(x = 2) (d) P(x = 3) (e) P(x = 4) (f) P(x =

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