Probability Distributions BINOMIAL DISTRIBUTION. Binomial Trials There are a specified number of repeated, independent trials There are a specified number.

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Presentation transcript:

Probability Distributions BINOMIAL DISTRIBUTION

Binomial Trials There are a specified number of repeated, independent trials There are a specified number of repeated, independent trials The outcome of Binomial experiments or Trials are either a Success or Failure The outcome of Binomial experiments or Trials are either a Success or Failure The Probability of Success is the same in each trial The Probability of Success is the same in each trial The Random Variable is the number of successes in a given number of trials The Random Variable is the number of successes in a given number of trials These are also called Bernoulli Trials These are also called Bernoulli Trials

Examples A coin is flipped A test of true and false questions A test of multiple choice questions Pulling a block out of a bag that contains 5 red blocks and 7 blue blocks Are all binomial probability experiments

Binomial Distribution Problem A coin is tossed 3 times. What is the probability distribution for the experiment? a) Define success for this experiment and list all the possible outcomes. b) What is the probability of success? Probability of failure? c) Define the random variable. d) Draw a tree diagram to determine the probability distribution. e) Complete the probability distribution for each outcome.

a) Define success for this experiment and list all the possible outcomes. A success for this experiment will be getting a tail There are only 2 possible outcomes for this experiment You get a Head or You get a Tail

b) What is the probability of success? Probability of failure?

d) Draw a tree diagram to determine the probability distribution

e) Complete the probability distribution for each outcome. Range of X 0123 P(x) according to Tree Diagram

Probability in a Binomial Distribution p is the probability of a success q is the probability of a failure n is the number of trials x is the outcome

Lets look back at our Example….Can we find the P(x) using our Binomial Distribution Ran ge of X 0123 P(x) Tree Diag ram P(x) Bino mial Distr ibuti on

Handout Question!!!!

Expectation for Binomial Distribution Since the probability for all n trials is the same the expectation for a success in any trial is p.

Homework! Pg 385 # 1, 3 5,7,10