Informal Geometry Period 1

1
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 likes
  McDonalds or Burger King?
• 3. What is the probability that a randomly chosen
  person is female or likes McDonalds?

McDonalds Burger King Wendys
Male 20 15 10
Female 20 10 25
7/20
65/100 13/20
3/4
2
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.
3
Probability

• Conditional Probability and Independent vs.
  Dependent events

4
Conditional Probability

• A conditional probability is the probability of
  an event occurring, given that another event has
  already occurred. The conditional probability of
  event B occurring, given that event A has
  occurred, is denoted by P(B/A) and is read as
  probability of B, given A.
• This is an and question, and solved by
  multiplication

5
Conditional Probability

• Two cards are selected in sequence from a
  standard deck. Find the probability that the
  second card is a queen, given that the first card
  is a king, and we did not replace the king.
• Because the first card is a king and is not
  replaced, the remaining deck has 51 cards, 4 of
  which are queens, so P(B/A) 4/51 ? 0.0078

6
Conditional Probability
Gene Present Gene Not Present Total
High IQ 33 19 52
Normal IQ 39 11 50
Total 72 30 102

• The above table shows the results of a study in
  which researchers examined a childs IQ and the
  presence of a specific gene in the child. Find
  the probability that a child has a high IQ, given
  that the child has the gene.

7
Conditional Probability
Gene Present Gene Not Present Total
High IQ 33 19 52
Normal IQ 39 11 50
Total 72 30 102

• There are 72 children who have the gene so the
  sample space consists of these 72 children. Of
  these, 33 have a high IQ, so
• P(B/A) 33/72 ? 0.458

8
Conditional Probability
Gene Present Gene Not Present Total
High IQ 33 19 52
Normal IQ 39 11 50
Total 72 30 102

• Find the probability that a child does not have
  the gene.
• P(child does not have the gene) 30/102
• Find the probability that a child does not have
  the gene, given that the child has a normal IQ
• P(B/A) 11/50

9
Blood Type Blood Type Blood Type Blood Type Blood Type
O A B AB Total
RH Factor Positive 156 139 37 12 344
RH Factor Negative 28 25 8 4 65
Total 184 164 45 16 409

• What is the probability of the blood being type B
  given it is positive?
• 37/344
• What is the probability of the blood being type
  RH Positive, given it is B or AB?
• (37 12)/(45 16) 49/61

10
Independent Events

• Two events A and B, are independent if the fact
  that A occurs does not affect the probability of
  B occurring.
• Then P(B/A) P(B)
• 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
• P(A and B)P(A)P(B)
  

11
Probability

• NOTE
• You add something to get the probability of
  something OR something
• You multiply something to get the probability of
  something AND something.

12
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

13
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

14
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) x P (yellow)
• 15 / 128

15
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 x 9/10 x 9/10 729/1000

16
Dependent Events

• 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 dont replace the first
  one.
• Probability of A and B occurring
• P(A and B)P(A)P(B/A)
  

17
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) x P
  (yellow)
• 1/8

18
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

19
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

20
Class Work

• Pg 353, 5 8 all and
• Handout 5-40 and 5-73 through 5-88