Warm up

1
Warm up

• Mr. Amica walks into ISS and takes 3 students out
  of the 15 in there to help him in the cafeteria.
  How many possibilities are there for picking the
  3 kids?
• 2. If he assigns jobs to each student where the
  first person has trash, the second sweeps, and
  the third puts up signs, how many possibilities
  are there now?

455
2730
2
Questions over hw?Textbookp. 349 1 10, 17,
18
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Daily Check
4
GPS AlgebraDay 4
UNIT QUESTION How do you use probability to make
plans and predict for the future? Standard
MM1D1, MM1D2, MM1D3 Todays Question When do I
add or multiply when solving compound
probabilities? Standard MM1D2.a,b.
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Practice with Conditional Probability
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The table gives the handedness and eyedness of a
randomly selected group of 100 people.
Right-Eyed Left-Eyed
Right-Handed 57 31
Left-Handed 6 6

1. If you randomly select a person from this group,
   what is the probability of getting a left-handed
   person?

7
The table gives the handedness and eyedness of a
randomly selected group of 100 people.
Right-Eyed Left-Eyed
Right-Handed 57 31
Left-Handed 6 6
2. If you randomly select a person from this
group, what is the probability of getting someone
who is left-eyed?
8
The table gives the handedness and eyedness of a
randomly selected group of 100 people.
Right-Eyed Left-Eyed
Right-Handed 57 31
Left-Handed 6 6
3. If you randomly select a LEFT-HANDED
person, what is the probability they are
left-eyed?
9
The table gives the handedness and eyedness of a
randomly selected group of 100 people.
Right-Eyed Left-Eyed
Right-Handed 57 31
Left-Handed 6 6
4. If you randomly select a LEFT-EYED person,
what is the probability they are left-handed?
10
The chart shows favorite subjects of students
based on their gender.
Math Science English SS
Male 46 42 13 25
Female 12 21 45 36
5. What is the probability that a randomly
chosen student likes history the most?
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The chart shows favorite subjects of students
based on their gender.
Math Science English SS
Male 46 42 13 25
Female 12 21 45 36
6. What is the probability that a randomly
chosen student is female?
12
The chart shows favorite subjects of students
based on their gender.
Math Science English SS
Male 46 42 13 25
Female 12 21 45 36
7. What is the probability that a randomly
chosen student both likes science and is a male?
13
The chart shows favorite subjects of students
based on their gender.
Math Science English SS
Male 46 42 13 25
Female 12 21 45 36
8. What is the probability that a randomly
chosen student likes social studies given that
they are a female?
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Compound Event

• A compound event combines two or more events,
  using the word and or the word or.

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AND

• Means you MULTIPLY

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OR

• Means you ADD

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Mutually Exclusivevs.Overlapping Events
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Mutually Exclusive

• two or more events cannot occur at the same time
• They have no common outcomes.

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For Mutually Exclusive Events

• Find the probability of each and ADD
• P(A or B) P(A) P(B)

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Mutually Exclusive Events

• Example 1Using a standard deck of 52 cards
  Find the P(4 or Ace).

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Mutually Exclusive Events

• Example 2When rolling two dice, what is P(sum
  of 4 or sum of 5)?

1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
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Mutually Exclusive Events

• Example 3Find the P(Red Queen or King).

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Overlapping

• events have at least one common outcome.
• You will have to SUBTRACT out the overlapping
  amount

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Overlapping Events
P(A or B) P(A) P(B) P(A and B)
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Overlapping Events

• Example 4
• Find the P(King or Clubs)?

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Overlapping Events

• Example 5
• Find the P(female or FL) out of the committee
  members listed in the table.

Fem Male
FL 8 4
AL 6 3
GA 7 3
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Overlapping Events

• Example 6
• When rolling 2 dice, what is the
  P(even sum or a number greater than 10)?

1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
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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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AND

• Means you MULTIPLY

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Example 1

• A coin is tossed and a 6-sided die is rolled.
• Find P(landing on heads and rolling a 3).

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Example 2

• A card is chosen at random from a deck of 52
  cards. It is then REPLACED and a second card is
  chosen.
• Find the P(a jack and an 8).

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Example 3

• A jar contains 3 red, 5 green, 2 blue and 6
  yellow marbles. A marble is chosen at random from
  the jar. After replacing it, a second marble is
  chosen.
• Find the P(a green and a yellow).

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Example 4

• A school survey found that 9 out of 10 students
  like pizza.
• If 3 students are chosen at random with
  replacement, find P(all three students like
  pizza).

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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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Example 5

• A jar contains 3 red, 5 green, 2 blue and 6
  yellow marbles. A marble is chosen at random from
  the jar.
• A second marble is chosen without replacing the
  first one.
• Find P(a green and a yellow marble).

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Example 6

• An aquarium contains 6 gold fish and 4 white
  fish. You randomly select a fish from the tank,
  do not replace it, and then randomly select a
  second fish.
• Find the P(1st fish is gold and 2nd fish is
  gold).

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Example 7

• 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.
• What is the P(1st part is bad and 2nd part is
  bad) if he doesnt replace the first?

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Conditional Probability

• A math teacher gave her class two tests. 25 of
  the class passed both tests and 42 of the class
  passed the first test. What percent of those who
  passed the first test also passed the second
  test?
• 60

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Conditional Probability

• A jar contains black and white marbles. Two
  marbles are chosen without replacement. The
  probability of selecting a black marble and then
  a white marble is 0.34, and the probability of
  selecting a black marble on the first draw is
  0.47. What is the probability of selecting a
  white marble on the second draw, given that the
  first marble drawn was black?
• 72

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Conditional Probability

• The probability that it is Friday and that a
  student is absent is 0.03. Since there are 5
  school days in a week, the probability that it is
  Friday is 0.2. What is the probability that a
  student is absent given that today is Friday?
• 15

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Conditional Probability

• At Kennedy Middle School, the probability that a
  student takes Technology and Spanish is 0.087.
  The probability that a student takes Technology
  is 0.68. What is the probability that a student
  takes Spanish given that the student is taking
  Technology?
• 13

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Workbook

• p. 369 1 6

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Mutually exclusive or overlapping?
1
2
3
4
P(A or B)
1
2
3
4
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Mutually exclusive or overlapping?
1
2
3
4
P(A or B)
1
2
3
4
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Mutually exclusive or overlapping?
1
2
3
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P(A or B)
1
2
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4
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Mutually exclusive or overlapping?
1
2
3
4
P(A or B)
1
2
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4
47
Mutually exclusive or overlapping?
1
2
3
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P(A or B)
1
2
3
4
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Mutually exclusive or overlapping?
1
2
3
4
P(A or B)
1
2
3
4
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HomeWork p. 353 1 4, 7 p. 354 1 4 Quiz
Monday