Warm up

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Warm up

• The following table shows the number of people
  that like a particular fast food restaurant.
• What is the probability that a person likes
  Wendys?
• What is the probability that a person is male?
• 3. What is the probability that a randomly chosen
  is male and likes Burger King?

McDonalds Burger King Wendys
Male 20 15 10
Female 20 10 25
7/20
45/100 9/20
15 / 100 3/20
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Questions over HW?
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Math I
UNIT QUESTION How do you use probability to make
plans and predict for the future? Standard
MM1D1-3 Todays Question When do I add or
multiply when solving compound probabilities? Stan
dard MM1D2.a,b.
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Independent vs. Dependent events

• Replacement and Without Replacement

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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)
  

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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

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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

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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

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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

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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).

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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
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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?

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

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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
  doesnt replace the first?

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

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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) ______ ________ ______ ______
  ______

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• 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) ___________
  _________________
• _________ ___________
  ________________

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Benchmark 2-2
The graph shows the path of a golf ball.
What is the range of the function?
b

• 0ltylt200 b) 0y 200
• c) 0y 7 d) 0ltylt7

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Benchmark 2-3
Which of the following is NOT true of a
parallelogram?

1. Any two opposite sides are congruent.
2. Any two opposite angles are congruent.
3. The diagonals bisect each other.
4. Any two consecutive angles are complimentary.

d
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Classwork textbook

• p. 353 5, 6
• p. 354 5, 6, 8

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Homework

• Complete
• GO1 and GO2