Homework Questions. Binomial Theorem Binomial  Bi – means 2 – two outcomes  Win/lose, girl/boy, heads/tails  Binomial Experiments.

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Homework Questions

Binomial Theorem

Binomial  Bi – means 2 – two outcomes  Win/lose, girl/boy, heads/tails  Binomial Experiments

The following have to be true:  The trials are independent  Each trial has two outcomes  P(S) or P(F)  P(success) or P(failure)  The probability of success is the same for each trial. The probability of failure is 1-p

Ex 1  In a basketball contest, each player is allowed 3 free-throws. If a certain individual has a 70% chance of making each free-throw, what is the probability of making exactly 2 out of 3?

Probability Formula  In a binomial experiment, P (r successes in n trials) = p = probability of success q = 1-p is the probability of failure

Go back to #1

Ex 2  A lottery consists of choosing a number from 000 to 999. All digits of the number must be matched in order, so the probability of winning is 1/1000=.001. A ticket costs $1, and the prize is $500. Suppose you play the lottery 1000 times in a row.  Write a probability distribution for the number of wins  What is the probability that you will break even?

a) Outcome 0 wins 1 win 2 wins 3 wins 4 wins 5+ win Probability

b)

Example 3  Morgan is taking a 10 question multiple choice test but has not studied. Each question has 4 possible responses, only one of which is correct. Find the probability of getting the results below if he answers all questions randomly.  Exactly 6 questions correct.  4 or fewer questions correct.  8 or more questions correct.  Enough to pass…

Answers a) a) b) b) c) c) d) d)

Homework  Worksheet