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Warm up
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 is male?
45/100 = 9/20
3. What is the probability that a randomly chosen is male and
likes Burger King?
15 / 100 = 3/20
Questions over HW?
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.
Independent vs.
Dependent events
Replacement and Without Replacement
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)
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)  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  9/10  9/10 = 729/1000

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).
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
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

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

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) = ______ ∙________ = ______ ∙ ______ = ______
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) = ___________ ∙ _________________
= _________ ∙ ___________ = ________________
Benchmark #2-2
The graph shows the path of a golf ball.
b
What is the range of the function?
a) 0<y<200
b) 0≤y ≤200
c) 0≤y ≤7
d) 0<y<7
Benchmark #2-3
Which of the following is NOT true of a parallelogram?
a) Any two opposite sides are congruent.
b) Any two opposite angles are congruent.
c) The diagonals bisect each other.
d) Any two consecutive angles are complimentary.
d
Classwork textbook
p. 353 #5, 6
p. 354 #5, 6, 8
Homework:
Complete
GO#1 and GO#2