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Binomial Distribution Characteristics of a Binomial Experiment (or called Bernoulli Experiment) i) ___________________________________________________ ___________________________________________________ ii) ___________________________________________________ ___________________________________________________ iii) ___________________________________________________ ___________________________________________________ iv) ____________________________________________________ ___________________________________________________ Note: If the random variable X is the number of “successes” in n Bernoulli trials with each trial having probability p of “success” and probability q of “failure” then The expectation of the number of successes in a binomial distribution of n Bernoulli trials with probability p of success on each trial is ________________. Example 1 Determine a probability function(model) for the number of heads when tossing a fair coin five times. Determine the expected number of heads using the formula and the definition of expected. Verify that the sum of the probabilities equals 1. Let X rep the random variable that represent the number of heads Outcome X P(X=x) xp(x) Example 2 A test consists of 10 multiple choice questions each with 5 possible answers, of which only one is correct. If the result of each question is chosen by random guessing, what is the probability that 6 of the answers chosen will be correct? Example 3 A bag contains 10 red marbles and 20 black marbles. A marble is chosen at random from the bag. Its colour is noted and then it is returned to the bag. This process is repeated 5 times. Find the probability of: a) selecting a red marble exactly 3 of the 5 times b) selecting a black marble 4 or more times Example 4 In a computer chip factory, 35 out of every 1000 chips produced are defective. A batch of 20 chips is chosen at random. a)What is the probability that at most 10% of the chosen chips are defective? b) Determine the expected number of defective chips