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4.2B –Binomial Distributions

4.2B –Binomial Distributions. Binomial Experiments : Experiment meeting the following criteria: 1) Repeated for a fixed number of trials, n . 2) 2 Possible outcomes: Success, S Failure, F 3) Probability for success is SAME for each trial

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4.2B –Binomial Distributions

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  1. 4.2B –Binomial Distributions • Binomial Experiments: Experiment meeting the following criteria: • 1) Repeated for a fixed number of trials, n. • 2) 2 Possible outcomes: • Success, S • Failure, F • 3) Probability for success is SAME for each trial • 4) Random variable, x, counts # of successful trials

  2. Binomial Probability Formula • n = # of trials • p = P(S) = Probability of success in 1 trial • q = P(F) = Probability of failure in 1 trial • x = # of successes in n trials P(x) = nCx(p)ᵡ(q)ᶮ ᵡ

  3. Find the Binomial Probabilities P(x) = nCx(p)ᵡ(q)ᶮ ᵡ • Rolling a six sided die: • 12 trials • Success is rolling a 6 (all other #’s are failure) • Probability of success in 1 trial = ________ • Probability of failure in 1 trial = _________ • Find probability of 2 successes (x=2)

  4. Find the Binomial Probabilities P(x) = nCx(p)ᵡ(q)ᶮ ᵡ • Drawing a card from a deck of 52 WITH replacement. • 20 trials • Success is drawing a HEART • Probability of success in 1 trial = ___________ • Probability of failure in 1 trial = ____________ • Find probability of 5 successes (x=5)

  5. Find the Binomial Probabilities P(x) = nCx(p)ᵡ(q)ᶮ ᵡ • Shooting free throws • 10 trials • Success is making the shot • Probability of success in 1 trial = __________ • Probability of failure in 1 trial = ___________ • Find probability of making 5 shots (x=5)

  6. Summary • Die: Probability of success in 1 trial = 1/6 = .17 • Probability of 2 successes _____ • My success results ______/12 = _____ • Total class results ______/______ = _____ • Class total with 2 successes ____/____ = ____

  7. Summary • Cards: Probability of success in 1 trial= ¼= .25 • Probability of 5 successes ________ • My success results _____/20 = ________ • Total class results ______/ _______ = ______ • Class total with 5 successes _____/______ = _____

  8. Summary • Free Throws: Probability of success in 1 trial = ½ = .50 • Probability of 5 successes __________ • My success results ______/10 = ______ • Total class results _____/_____ = ______ • Class total with 5 successes ____/_____ = ______

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