1. 7/20 The following table shows the number of people that like a particular fast food restaurant. 1)What is the probability that a person likes Wendy’s? 2)What is the probability that a person is male given they like Burger King? 3. What is the probability that a randomly chosen person is female or likes McDonald’s? 3/5 McDonald’sBurger KingWendy’s Male201510 Female201025 3/4

2. Benchmark #1-4 Al Gone went on a long trip. The graph below represents the relationship between distance and time. During what interval was Al's average rate of travel the fastest? a)0 to 6b) 6 to 8 c) 8 to 11d) 11 to 16 b

3. Benchmark #1-5 a)b) a Which function has a higher rate of change?

4. Benchmark #1-6 a)b) c) d) c

5. Math I UNIT QUESTION: How do you use probability to make plans and predict for the future? Standard: MM1D1-3 Today’s Question: When do I add or multiply when solving compound probabilities? Standard: MM1D2.a,b.

6. Probability Independent vs. Dependent events

7. Independent Events Two events A and B, are independent if the fact that A occurs does not affect the probability of B occurring. Two events A and B, are independent if the fact that A occurs does not affect the probability of B occurring. Examples- Landing on heads from two different coins, rolling a 4 on a die, then rolling a 3 on a second roll of the die. Examples- Landing on heads from two different coins, rolling a 4 on a die, then rolling a 3 on a second roll of the die. Probability of A and B occurring: Probability of A and B occurring: P(A and B)=P(A)*P(B) P(A and B)=P(A)*P(B)

8. Experiment 1 A coin is tossed and a 6-sided die is rolled. Find the probability of landing on the head side of the coin and rolling a 3 on the die. A coin is tossed and a 6-sided die is rolled. Find the probability of landing on the head side of the coin and rolling a 3 on the die. P (head)=1/2 P (head)=1/2 P(3)=1/6 P(3)=1/6 P (head and 3)=P (head)*P(3) P (head and 3)=P (head)*P(3) =1/2 * 1/6 =1/2 * 1/6 = 1/12 = 1/12

9. Experiment 2 A card is chosen at random from a deck of 52 cards. It is then replaced and a second card is chosen. What is the probability of choosing a jack and an eight? A card is chosen at random from a deck of 52 cards. It is then replaced and a second card is chosen. What is the probability of choosing a jack and an eight? P (jack)= 4/52 P (jack)= 4/52 P (8)= 4/52 P (8)= 4/52 P (jack and 8)= 4/52 * 4/52 P (jack and 8)= 4/52 * 4/52 = 1/169 = 1/169

10. Experiment 3 A jar contains three red, five green, two blue and six yellow marbles. A marble is chosen at random from the jar. After replacing it, a second marble is chosen. What is the probability of choosing a green and a yellow marble? A jar contains three red, five green, two blue and six yellow marbles. A marble is chosen at random from the jar. After replacing it, a second marble is chosen. What is the probability of choosing a green and a yellow marble? P (green) = 5/16 P (green) = 5/16 P (yellow) = 6/16 P (yellow) = 6/16 P (green and yellow) = P (green) x P (yellow) P (green and yellow) = P (green) x P (yellow) = 15 / 128 = 15 / 128

11. Experiment 4 A school survey found that 9 out of 10 students like pizza. If three students are chosen at random with replacement, what is the probability that all three students like pizza? A school survey found that 9 out of 10 students like pizza. If three students are chosen at random with replacement, what is the probability that all three students like pizza? P (student 1 likes pizza) = 9/10 P (student 1 likes pizza) = 9/10 P (student 2 likes pizza) = 9/10 P (student 2 likes pizza) = 9/10 P (student 3 likes pizza) = 9/10 P (student 3 likes pizza) = 9/10 P (student 1 and student 2 and student 3 like pizza) = 9/10 x 9/10 x 9/10 = 729/1000 P (student 1 and student 2 and student 3 like pizza) = 9/10 x 9/10 x 9/10 = 729/1000

12. Dependent Events Two events A and B, are dependent if the fact that A occurs affects the probability of B occurring. Two events A and B, are dependent if the fact that A occurs affects the probability of B occurring. Examples- Picking a blue marble and then picking another blue marble if I don’t replace the first one. Examples- Picking a blue marble and then picking another blue marble if I don’t replace the first one. Probability of A and B occurring: Probability of A and B occurring: P(A and B)=P(A)*P(B/A) P(A and B)=P(A)*P(B/A)

13. Experiment 1 A jar contains three red, five green, two blue and six yellow marbles. A marble is chosen at random from the jar. A second marble is chosen without replacing the first one. What is the probability of choosing a green and a yellow marble? A jar contains three red, five green, two blue and six yellow marbles. A marble is chosen at random from the jar. A second marble is chosen without replacing the first one. What is the probability of choosing a green and a yellow marble? P (green) = 5/16 P (green) = 5/16 P (yellow given green) = 6/15 P (yellow given green) = 6/15 P (green and then yellow) = P (green) x P (yellow) P (green and then yellow) = P (green) x P (yellow) = 1/8 = 1/8

14. Experiment 2 An aquarium contains 6 male goldfish and 4 female goldfish. You randomly select a fish from the tank, do not replace it, and then randomly select a second fish. What is the probability that both fish are male? An aquarium contains 6 male goldfish and 4 female goldfish. You randomly select a fish from the tank, do not replace it, and then randomly select a second fish. What is the probability that both fish are male? P (male) = 6/10 P (male) = 6/10 P (male given male) = 5/9 P (male given male) = 5/9 P (male and then, male) = 1/3 P (male and then, male) = 1/3

15. Experiment 3 A random sample of parts coming off a machine is done by an inspector. He found that 5 out of 100 parts are bad on average. If he were to do a new sample, what is the probability that he picks a bad part and then, picks another bad part if he doesn’t replace the first? A random sample of parts coming off a machine is done by an inspector. He found that 5 out of 100 parts are bad on average. If he were to do a new sample, what is the probability that he picks a bad part and then, picks another bad part if he doesn’t replace the first? P (bad) = 5/100 P (bad) = 5/100 P (bad given bad) = 4/99 P (bad given bad) = 4/99 P (male and then, male) = 1/495 P (male and then, male) = 1/495

16. Class work Why did the actor jump out of a window in Times Square?

17. Homework Page 353 #5, 6 Page 354 #5, 6, 8 and Independent WS