Warm up 7/20 45/100 = 9/20 15 / 100 = 3/20 Male 20 15 10 Female 25 The following table shows the number of people that like a particular fast food restaurant. What is the probability that a person likes Wendy’s? What is the probability that a person is male? 3. What is the probability that a randomly chosen is male and likes Burger King? McDonald’s Burger King Wendy’s Male 20 15 10 Female 25 7/20 45/100 = 9/20 15 / 100 = 3/20

Questions over HW?

When do I add or multiply when solving compound probabilities? 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.

Independent vs. Dependent events Replacement and Without Replacement

Independent Events (with replacement) Two events A and B, are independent if the fact that A occurs does not affect the probability of B occurring. Probability of A and B occurring: P(A and B) = P(A)  P(B)

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. P (head)=1/2 P(3)=1/6 P (head and 3)=P (head)  P(3) =1/2  1/6 = 1/12

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? P (jack)= 4/52 P (8)= 4/52 P (jack and 8)= 4/52  4/52 = 1/169

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? P (green) = 5/16 P (yellow) = 6/16 P (green and yellow) = P (green)  P (yellow) = 15 / 128

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? P (student 1 likes pizza) = 9/10 P (student 2 likes pizza) = 9/10 P (student 3 likes pizza) = 9/10 P (student 1 and student 2 and student 3 like pizza) = 9/10  9/10  9/10 = 729/1000

Dependent Events (without replacement) Two events A and B, are dependent if the fact that A occurs affects the probability of B occurring. Not replacing will cause you to subtract from the denominator (and sometimes from the numerator).

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? P (green) = 5/16 P (yellow given green) = 6/15 P (green and then yellow) = P (green)  P (yellow) = 1/8

Experiment 2 P (male) = 6/10 P (male given 1st male) = 5/9 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 given 1st male) = 5/9 P (male and then, male) = 1/3

Experiment 3 P (bad) = 5/100 P (bad given 1st bad) = 4/99 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 given 1st bad) = 4/99 P (bad and then, bad) = 1/495

Independent or Dependent? You roll two number cubes. What is the probability that you roll a 1 first and an 2 second? Solution The events are ____________. The number on one number cube ____________affect the other. P(1 & 2) = ______ ∙________ = ______ ∙ ______ = ______

Markers A box contains 8 red markers and 3 blue markers Markers A box contains 8 red markers and 3 blue markers. You choose one marker at random, do not replace it, then choose a second marker at random. What is the probability that both markers are blue? Solution Because you do not replace the first marker, the events are ____________. Before you choose a marker, there are 11 markers, 3 of them are blue. After you choose a blue marker, there are 10 markers left and two of them are blue. So, the ________________ that the second marker is blue given that the first marker is blue is _____. P(blue and then blue) = ___________ ∙ _________________ = _________ ∙ ___________ = ________________

Benchmark #2-2 The graph shows the path of a golf ball. What is the range of the function? b 0<y<200 b) 0≤y ≤200 c) 0≤y ≤7 d) 0<y<7

Benchmark #2-3 Which of the following is NOT true of a parallelogram? Any two opposite sides are congruent. Any two opposite angles are congruent. The diagonals bisect each other. Any two consecutive angles are complimentary. d

Classwork textbook p. 353 #5, 6 p. 354 #5, 6, 8

Homework: Complete GO#1 and GO#2