1. Aim: How do we use binomial probability? Complete worksheet

2. What is a success? What is a failure? Successful Trials: (p) getting the wanted outcome Failure Trials: (1-p=q) getting the unwanted outcome

3. Combinations Combinations: a selection in which order is not important

4. Binomial Probability In general for a given experiment, if the probability of success in p and the probability of failure is 1 - p = q, then the probability of exactly r successes in n independent trials is

5. Binominal Probability: “Exactly” If a fair coin is tossed 10 times, what is the probability that it falls tails exactly 6 times? – Procedure: (1) Find the probability of getting the wanted outcome – P(tails) = 1/2 (2) Find the probability of getting the unwanted outcome – P(not tails) = 1/2 Put it into the formula

6. Binomial Probability: “At Least” A coin is loaded so that the probability of heads is 4 times the probability of tails. What is the probability of at least 1 tail in 5 throws? – Procedure: (1) probability of success – P(tails) = 1/5 (2) probability of failure – P(not tails) = 4/5 (3) at least = that number up to the max – P(at least 1 tail in 5) = P(1) + P(2) + P(3) + P(4) + P(5) (4) plug in formula and calculate

7. Binomial Probability: “at most” A family of 5 children is chosen at random. What is the probability that there are at most 2 boys in this family of 5? – Procedure: (1) probability of success – P(boys) = 1/2 (2) probability of failure – P(not boy) = 1/2 (3) at most = that number down to 0/min – P(at most 2 boys in 5) = P(2) + P(1) = P(0) (4) plug in formula and calculate