11.10 Binomial Probability Formula 751 Exercises Warm Up Exercises In Exercises 1– 4, fill in the blank with an appropriate word, phrase, or symbol(s). 1. In a binomial experiment, there are n repeated, independent ___________. Trials 2. Each trial in a binomial experiment has two possible outcomes, success and ___________. Failure 3. In the binomial probability formula, p represents the probability of ___________. Success 4. In the binomial probability formula, q represents the probability of ___________. Failure Practice the Skills In Exercises 5–10, assume that each of the n trials is independent and that p is the probability of success on a given trial. Use the binomial probability formula to determine P x( ). When necessary, round your answers to five decimal places. 5. n x p 6, 3, 0.2 = = = 0.08192 6. n x p 3, 2, 0.6 = = = 0.432 7. n x p 5, 2, 1 3 = = = 0.32922 8. n x p 6, 3, 3 7 = = = 0.29376 9. n x p 6, 0, 0.5 = = = 0.015625 10. n x p 5, 0, 0.6 = = = 0.01024 Problem Solving 11. A Dozen Eggs An egg distributor determines that the probability that any individual egg has a crack is 0.14. a) Write the binomial probability formula used to determine the probability that exactly x eggs of n eggs are cracked. P x C ( ) ( )(0.14) (0.86) n x x n x = − b) Write the binomial probability formula used to determine the probability that exactly 2 eggs in a onedozen egg carton are cracked. P C (2) ( )(0.14) (0.86) 12 2 2 10 = c) Evaluate the formula written in part (b). Round your answer to five decimal places. 0.28628 12. NFL Draft Picks According to NFL.com, 83% of draft picks play at least one down in the regular season for the team that drafted them. a) Write the binomial formula used to determine the probability that exactly x out of n randomly selected draft picks play at least one down in the regular season for the team that drafted them. = − P x C ( ) ( )(0.83) (0.17) n x x n x b) Write the binomial formula used to determine the probability that exactly 15 out of 18 randomly selected draft picks played at least one down for the team that drafted them. = P x C ( ) ( )(0.83) (0.17) 18 15 15 3 c) Evaluate the formula written in part (b). Round your answer to five decimal places. 0.24502 In Exercises 13–26, use the binomial probability formula to answer the question. When necessary round answers to five decimal places. 13. Tossing a Coin A fair coin is tossed 10 times. Determine the probability that the coin is heads exactly a) one time. 0.00977 b) five times. 0.24609 c) nine times. 0.00977 14. Tossing a Coin A fair coin is tossed 5 times. Determine the probability that the coin is heads a) zero times. 0.03125 b) at least one time. 0.96875 15. Balls in a Bin A bin contains 5 balls colored red, yellow, blue, orange, and purple, respectively. Anika randomly selects 4 balls with replacement. Determine the probability that she selects a) the red ball zero times. 0.4096 b) the red ball at least one time. 0.5904 16. Balls in a Bin A bin contains 5 balls colored red, yellow, blue, orange, and purple, respectively. Tristan randomly selects 7 balls with replacement. Determine the probability that he selects the yellow ball exactly a) one time. 0.36700 b) three times. 0.11469 c) five times. 0.00430 17. Asthma According to ACAAI.org, 8.3% of Americans have asthma. If 20 Americans are randomly selected, determine the probability that at least 1 has asthma. 0.82324 18. Haircut Tip Marcus is a barber and has learned that 75% of his customers tip him when they are paying for a SECTION 11.10 Debby Wong/Shutterstock
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