The Binomial Distribution. Introduction # correct TallyFrequencyP(experiment)P(theory) 0 1 2 3 Mix the cards, select one & guess the type. Repeat 3 times.

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Presentation transcript:

The Binomial Distribution

Introduction # correct TallyFrequencyP(experiment)P(theory) Mix the cards, select one & guess the type. Repeat 3 times per turn and record your results.

Introduction # correctTallyFrequencyP(experiment)P(theory) Repeat guessing 4 times – Graph the results

If the experiment were repeated for Guessing 9 times, how could we calculate the probabilities for each number correct? P(guess is correct) = 1 / 3 Number Correct

Binomial Formula for theory P(X =x) = n C x  x (1 -  ) n-x Where n is the number of trials.  is the probability of success.

Definition of the Binomial Distribution The Binomial Distribution occurs when: (a) There is a fixed number (n) of trials. (b) The result of any trial can be classified as a “success” or a “failure” (c) The probability of a success (  or p) is constant from trial to trial. (d) Trials are independent. If X represents the number of successes then: P(X =x) = n C x  x (1 -  ) n-x

PARAMETERS of binomial distribution Parameters = what describes the distribution ‘n’ Fixed number of trials. ‘  ’ or ‘p’ The probability of a success.

Example #1 a)Flipping a coin 8 times – what is the probability that exactly 3 of them are heads? b) Does this experiment meet the conditions of a binomial distribution?

Example #2 Calculate the probability of a drawing pin landing on its back 3 times in 5 trials if the probability of getting a drawing pin to land on its back on any toss is 0.4 Let X be a random variable representing the number of “backs” in 5 tosses of the drawing pin. Then X is binomial with n = 5,  = 0.4. (i) By formula: P(X = 3) = 5 C 3 × × = (ii) Using tables: P(X = 3) We want P(X = 3).