Transcript Independent and Dependent Events f09

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?
2) What is the probability that a person is male given they like
Burger King?
7/20
3/5
3. What is the probability that a randomly chosen person is female
3/4
or likes McDonald’s?
Benchmark #1-4
Al Gone went on a long trip. The graph below represents the relationship between
distance and time. During what interval was Al's average rate of travel the fastest?
b
a) 0 to 6
b) 6 to 8
c) 8 to 11
d) 11 to 16
Benchmark #1-5
Which function has a higher rate of change?
a)
b)
a
Benchmark #1-6
c
a)
b)
c)
d)
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
Independent vs.
Dependent events
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.
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)
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) x 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 x 9/10 x 9/10 = 729/1000

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 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

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 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 doesn’t replace the
first?
P (bad) = 5/100
P (bad given bad) = 4/99
P (male and then, male) = 1/495

Class work
Why did the actor jump out of
a window in Times Square?
Homework
Page 353 #5, 6
Page 354 #5, 6, 8
and Independent WS