Transcript Conditional Probability

The following table shows the number of people that like a particular
fast food restaurant.
McDonald’s
Burger King
Wendy’s
Male
20
15
10
Female
20
10
25
1) What is the probability that a person likes Wendy’s?
7/20
2) What is the probability that a person likes McDonald’s or Burger
King?
65/100 = 13/20
3. What is the probability that a randomly chosen person is female
or likes McDonald’s?
3/4
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.
Probability
Conditional Probability
and Independent vs.
Dependent events
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
Conditional Probability
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
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
Conditional Probability
Gene
Present
High IQ
33
Normal IQ 39
Total
72

Gene Not
Present
19
11
30
Total
52
50
102
The above table shows the results of a study in
which researchers examined a child’s 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.
Conditional Probability
Gene
Present
High IQ
33
Normal IQ 39
Total
72


Gene Not
Present
19
11
30
Total
52
50
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
Conditional Probability
Gene Not
Present
19
Total
High IQ
Gene
Present
33
Normal IQ
39
11
50
Total
72
30
102
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
52
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
RH
Factor




Positive
Negative
Total
O
156
28
184
Blood Type
A
B AB Total
139 37 12 344
25
8
4
65
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
Independent Events


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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)
Probability



NOTE:
You add something to get the probability of
something OR something
You multiply something to get the probability of
something AND something.
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

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
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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 x 9/10 x 9/10 = 729/1000

Dependent Events
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
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.
Probability of A and B occurring:
P(A and B)=P(A)*P(B/A)
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
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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
st
P (male given 1 male) = 5/9
P (male and then, male) = 1/3

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?
P (bad) = 5/100
P (bad given 1st bad) = 4/99
P (bad and then, bad) = 1/495
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Class Work
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Pg 353, # 5 – 8 all and
Handout: # 5-40 and 5-73 through 5-88