1. Warm-Up #9 (Tuesday, 2/23/2016) 1.(Use the table on the left) How many students are in the class? What fraction of the students chose a red card? ResultFrequency Hearts5 Diamonds9 Spades8 Clubs6 2. Pooja is tossing coins. What is the probability of her tossing 6 coins one after the other and getting heads on the first 3 coins and tails on the last three turns? Determine the type of events and answer the question. 3. Randall bought a bag of Sour Patch Kids that contained 6 red, 18 blue, and 9 green. What is the probability of Randall reaching into the bag and pulling out blue or green Sour Patch Kids and then reaching in again without replacing the first one and pulling out a red one? Determine the type of events and answer the question.

2. Homework Monday, 2/22 Independent and Dependent packet. FINISH ALL

3. Independent And Dependent Events

4. Today’s Objective Students will distinguish between events that are dependent and independent and solve probability problems involving these events.

5. Independent and Dependent Events Independent Events: Two events are said to be independent when one event has NO AFFECT on the probability of the other event occurring. Dependent Events: Two events are dependent if the outcome or probability of the first event AFFECTS the outcome or probability of the second. GAME TIME!

6. Determine Whether The Events Are Independent or Dependent: 1.Selecting a marble from a container and selecting a jack from a deck of cards. Independent 2.Rolling a number less than 4 on a die and rolling a number that is even on a second die. Independent 3.Choosing a jacket from a deck of cards and choosing another jack, without replacement. dependent 4.Picking a red marble from a bag and then picking a blue marble, without replacement. dependent 5.Picking a red marble from a bag and then replace it back to pick a blue marble. Independent

7. Example 1 Suppose a die is rolled and then a coin is tossed Are these events dependent or independent? They are independent because the outcome of rolling a die does not affect the outcome of tossing a coin, and vice versa. We can construct a table to describe the sample space and probability ROLL 1ROLL 2ROLL 3ROLL 4ROLL 5ROLL 6 HEAD TAIL

8. How many outcomes are there for rolling the die? 6 outcomes How many outcomes are there for tossing the coin? 2 outcomes How many outcomes are these in the sample space of rolling the die and tossing the coin? 12 outcomes What is the relationship between the number of outcomes of each event and the number of outcomes in the sample space? Multiply the number of outcomes in each event together to get the total number of outcomes ROLL 1ROLL 2ROLL 3ROLL 4ROLL 5ROLL 6 HEAD1, H2, H3, H4, H5, H6, H TAIL1, T2, T3, T4, T5, T6, T

9. a. What is P(3)? 2/12 b. What is P(tails)? 6/12 c. What is P(3 AND tails)? 1/12 d. What is P(even)? 6/12 ROLL 1ROLL 2ROLL 3ROLL 4ROLL 5ROLL 6 HEAD1, H2, H3, H4, H5, H6, H TAIL1, T2, T3, T4, T5, T6, T e. What is P(heads)? 6/12 f. What is P(even And heads)? 3/12 g. What do you notice about the answers to c and f?

10. Probabilities of Independent Events

11. Examples Plans After High School GenderUniversityCommunity CollegeTotal Males285684 Females433780 Total7193164

12. Examples Plans After High School GenderUniversityCommunity CollegeTotal Males285684 Females433780 Total7193164

13. Suppose a card is chosen at random from a deck of cards, replaced, and then a second card is chosen.

14. Probabilities Dependent Events Remember we said earlier that Dependent Events: two events are dependent if the outcome or probability of the first event affects the outcome or probability of the second. We cannot use the multiplication rule for finding probabilities of dependent events like we did with independent events because the first event affects the probability of the other event occurring. Instead, we need to think about how the occurrence of the first event will affect the sample space of the second event to determine the probability of the second event occurring. Then we can multiply the new probabilities.

15. Examples 1.Suppose a card is chosen at random from a deck, the card is NOT replaced, and then a second card is chosen from the same deck. What is the probability that both will be 7s? This is similar to the earlier example, but these events are dependent. How do we know? How does the first event affect the sample space of the second event?

17. 2. A box contains 5 red marbles and 5 purple marbles. What is the probability of drawing 2 purple marbles and 1 red marble in succession without replacement?

18. 3. A box contains 5 red marbles and 5 purple marbles. What is the probability of first drawing all 5 red marbles in succession and then drawing all 5 purple marbles in succession without replacement?