3 4 The Binomial Distribution Binomial Trials A

3. 4 The Binomial Distribution

Binomial Trials A binomial experiment has the properties: 1. The number of trials in the experiment is fixed. 2. The only outcomes are “success” and “failure. ” 3. The probability of success in each trial is the same. 4. The trials are independent of each other.

Probabilities in Bernoulli Trials In a binomial experiment in which the probability of success in any trial is p, the probability of exactly x successes in n independent trials is given by

Ex 1. A card is drawn from a standard 52 -card deck. If drawing a club is considered a success, find the probability of a. exactly one club in 4 draws (with replacement). b. no clubs in 5 draws (with replacement). c. At least 3 clubs in 5 draws (with replacement).

Mean, Variance, and Standard Deviation of a Random Variable X If X is a binomial random variable associated with a binomial experiment consisting of n trials with probability of success p and probability of failure q, then the mean variance, and standard deviation of X are

Ex 2. A baseball player has a 0. 241 batting average. a) In 40 at-bats, how many hits is he expected to make. b) Find the standard deviation.

Ex 3: If the probability that a certain tennis player will serve an ace is 1/4, what is the probability that she will serve exactly two aces out of five serves?

Ex 4: From experience, the manager at a book store knows that 40% of the people who are browsing the store will make a purchase. What is the probability that among ten people who are browsing the store, at least three will make a purchase?