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Bernoulli Trials

The Binomial Distribution. Bernoulli Trials A Bernoulli trial is a random experiment with only 2 possible outcomes . e.g. tossing a coin, throw a 6 when a die is thrown.

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Bernoulli Trials

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  1. The Binomial Distribution Bernoulli Trials A Bernoulli trial is a random experiment with only 2 possible outcomes. e.g.tossing a coin,throw a 6 when a die is thrown. The outcomes of these trials are called ‘success’ and ‘failure’ and the probability distribution for these trials is called the Binomial Distribution.

  2. If X has a binomial distribution, we write X ~ B ( n , p ) n = number of trials p = probability of success P(X = x) q = probability of failure (q = 1 – p)

  3. Example • A die is thrown 8 times. Calculate the probability that a score of 6 is obtained • exactly 3 times, • at least 7 times, • at least twice. X ~ B ( 8 , ) a) P(X = 3) = 56 x 0.0046 x 0.40188 = 0.1042

  4. b) P(X ≥ 7) = P(X = 7) + P(X = 8) = 0.0000238 + 0.000000595 = 0.00002441 c) P(X ≥ 2) = 1 – P(X < 2) = 1 – [P(X = 0) + P(X = 1)] = 1-(0.232568 + 0.37210886) = 0.395323

  5. Exercise 4.5a Mathematics Statistics Unit S1 - WJEC

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