Lesson 15-8: Probabilities with two or more activities
Date ___________
p.617-627
Without Replacement: P(A and B) = P(A) * P(B given that A has occurred). These
events are dependent. (ex: cards,
)
With Replacement: P(A and B) = P(A) * P(B). These are independent events.
Conditional Probability: computing probabilities with or without replacement are
conditional because you must compute the second probability given that the first
P A and B   P A   P B | A 
probability has occurred.
P B | A  
P A and B 
P A 
Ex 1| A box contains one red, one blue, one green, and one yellow marble. Two
marbles are drawn without replacement. Find P(R followed by Y).
Ex 2| Three fair dice are thrown. What is the probability that all three dice show
a 5?
Ex 3| If two cards are drawn from an ordinary deck without replacement, what is
the probability that the cards form a pair (two cards of the same face value but
different suits)?
533573259, pg.1
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Ex 4| A jar contains four white marbles and two blue marbles, all the same size. A
marble is drawn at random and not replaced. A second marble is them drawn from
the jar. Find the probability that:
a) both are white
b) both are blue
c) both are the same
Ex 5| A fair die is rolled.
a) Find the probability that the die shows a 4 given that the die shows an
even number.
b) Find the probability that the die shows a 1 given that the die shows a
number less than 5.
533573259, pg.2
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Ex 6| Fred has two quarters and one nickel in his pocket. The pocket has a hole in
it, and a coin drops out. Fred picks up the coin and puts it back into his pocket. A
few minutes later, a coin drops out of his pocket again.
a. Draw a tree diagram or list the sample space for all possible pairs that
are outcomes to describe the coins that fell.
b. What is the probability that the same coin fell out of Fred’s pocket
both times?
c. What is the probability that the two coins that fell out have a total
value of 30 cents?
d. What is the probability that a quarter fell out at least once?
533573259, pg.3
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Ex 7| Of Roosevelt High School’s 1,000 students, 300 are athletes, 200 are in the
Honor Roll, and 120 play sports and are in the Honor Roll. What is the probability
that a randomly chosen student who plays a sport is in the Honor Roll?
HW: p.624/3-20 4’s
533573259, pg.4