1. Chapter 12 – Probability and Statistics 12.4 – Multiplying Probabilities

2. Today we will learn how to: Find the probability of two independent events Find the probability of two dependent events

3. 12.4 – Multiplying Probabilities In a situation with two events, you can find the probability of both events occurring if you know the probability of each event occurring

4. 12.4 – Multiplying Probabilities Probability of Two Independent Events If two events, A and B, are independent, then the probability of both events occurring is P(A and B) = P(A) · P(B) This can be applied to any number of independent events

5. 12.4 – Multiplying Probabilities Example 1 Gerardo has 9 dimes and 7 pennies in his pocket. He randomly selects one coin, looks at it, and replaces it. He then randomly selects another coin. What is the probability that both coins he selects are dimes?

6. 12.4 – Multiplying Probabilities Example 2 When three dice are rolled, what is the probability that the first two show a 5 and the third shows an even number?

7. 12.4 – Multiplying Probabilities Probability of Dependent Events In Example 1, what is the probability that Gerard selects two dimes if he does not put his first dime back? These two events are dependent because the outcome of the first event affects the outcome of the second event

8. 12.4 – Multiplying Probabilities Probability of Two Dependent Events If two events, A and B, are dependent, then the probability of both events occurring is P(A and B) = P(A) · P(B following A) This formula can be extended to any number of dependent events

9. 12.4 – Multiplying Probabilities Example 3 The host of a game show is drawing chips from a bag to determine the prizes for which contestants will play. Of the 20 chips in the bag, 11 say computer, 8 say trip, and 1 says truck. If the chips are drawn at random without replacement, find the probability of drawing a computer, then a truck.

10. 12.4 – Multiplying Probabilities Example 4 Three cards are drawn from a standard deck of cards without replacement. Find the probability of drawing a heart, another heart, and a spade in that order.

11. 12.4 – Multiplying Probabilities HOMEWORK Page 706 #13 – 29 odd, #30 – 35