Binomial Distributions ALGEBRA 2 LESSON 12-6 12- 6 Binomial Distributions A binomial experiment has three important features: The situation involves repeated trials Each trial has two possible outcomes (success or failure) The probability of success is constant throughout the trials (The trials are independent) 12-6

Binomial Distributions ALGEBRA 2 LESSON 12-6 A fast food restaurant is attaching prize cards to every one of its soft drink cups. The restaurant awards free drinks as prizes on three out of four cards. Suppose you have three cards. Find the probability that exactly one of these cards will reveal a prize. Each card represents a trial with a probability of success of . The probability of failure is . The tree diagram shows the probabilities along each path. 3 4 1 P (three prizes) = 1 = 0.422 3 4 P (two prizes) = 3 = 0.422 3 4 2 1 P (one prize) = 3 = 0.141 3 4 1 2 P (no prize) = 1 = 0.016 1 4 3 The probability that exactly one of three cards will reveal a free drink is about 14%. 12-6

Binomial Distributions ALGEBRA 2 LESSON 12-6 Alicia walks to school with her friend Juana. Juana is on time 80% of the time. What is the probability that Juana will be on time five days in a row? Relate:  This is a binomial experiment. • There are five days. • Each day she’ll be on time or late. • The probability of on time is 0.8 for each day. Define: Let n = 5 (n= number of trials). Let p = 0.8 (p = probability of success). Let q = 0.2 (q = probability of failure). Let x = 5 (x = number of successes). Write: nCxpxqn–x = 5C5(0.8)5(0.2)0 Substitute. = (1)(0.8)5(1) Simplify. = 0.32768 Simplify. The probability that she will be on time five days in a row is about 33%. 12-6