1. Binomial Distributions

2. Binomial Experiments Have a fixed number of trials Each trial has tow possible outcomes The trials are independent The probability of each outcome is constant

3. Example Suppose a basketball player is shooting free throws. He has hit (H) about 90% of his free throws this season. Use a tree diagram to find the probability that he will make one of two free throws to win the game.

4. Binomial Probability

5. Example As part of a promotion, a store is giving away scratch-off cards. Each card has a 40% chance of awarding a prize. Suppose you have five cards. Find the probability that exactly four of the five cards will reveal a prize.

6. Binomial Theorem You can use binomial expansions to find binomial probabilities.

7. Expand using the binomial theorem

8. Each hour at a cell phone factory, Quality Control (QC) tests the durability of four randomly selected phones. If more than one fails, QC rejects the entire production for that hour. If in one hour 95% of the phones made are acceptable, what is the probability that QC rejects that hour’s phone production?

9. Example A multiple-choice quiz has five questions. Each question has four answer choices. If you guess every answer, what is the probability of getting at least three correct?

10. Practice