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Handout - Chapter 8
Math 166
Section 8-1
Ex 1. Out of the last 1500 students that have had Rob as an instructor, 342 got A's.
What is the probability of one of Rob's current students getting an A?
Ex 2. Rob has a deck of 40 cards, numbered 1 through 40. The first 10 are black,
the next 20 are red, and the last 10 are green. You randomly pick 4 cards from
the deck. What is the probability that
a) all 4 cards are green?
b) all 4 cards are odd-numbered?
c) one card is black and 3 cards are red?
d) you got the cards numbered 10, 20, 30, & 40?
e) you got the cards numbered 10, 20, 30, & 40, in that order?
Ex 3. Rob has 2 fair dice (not weighted) - one is numbered 2 through 6 with an
extra 6, and the other is numbered 4 through 6, with two of each number. You
roll the dice and add the numbers facing up. What is the probability of getting
a) 12?
b) 9?
c) 6?
d) 4?
Section 8-2
Ex 1. Rob has a deck of 40 cards, numbered 1 through 40. The first 10 are black,
the next 20 are red, and the last 10 are green. You randomly pick one card from
the deck. What is the probability that it is
a) at least 25 or red?
b) less than 5 or green?
Ex 2. Rob deals you 5 cards from his deck of 40 cards (see Ex 1). What is the
probability that at least one of the cards is green?
Ex 3. Rob has a fair die numbered 1 through 5, with an extra 1. What are the odds
for and against rolling an even number?
8
3
Ex 4. The odds against an event E occurring are . Find the probability of E.
€
Section 8-3
Ex 1. You pick one card from a standard 52-card deck. What is the probability
that it’s a jack, given that it’s a face card?
Ex 2. A jar contains 200 marbles, as summarized in the table:
Yellow
Green
Blue
Total
Striped
40
45
10
95
Not Striped
50
30
25
105
Total
90
75
35
200
a) If you pick one marble from the jar, what is the probability that it is
yellow, given that it’s striped? striped, given that it’s yellow?
b) If you pick two marbles, without replacement, what is the probability that
the first is yellow and the second is blue?
c) If you pick two marbles, with replacement, what is the probability that
they’re both blue?
Ex 3. Rob has 5 cards - 3 black & 2 red. You pick two of the cards, without
replacement. Find the probability for each possible pair of colors using a
probability tree.
Section 8-4
Ex 1. Urn 1 contains 3 red and 7 blue marbles
Urn 2 contains 3 red and 2 blue marbles
Rob randomly picks an urn, then randomly picks a marble from that urn.
a) If Rob picked a blue marble, what is the probability that it came from Urn 1?
b) If Rob picked a red marble, what is the probability that it came from Urn 2?
Ex 2. Using the original urns from Ex 1, Rob picks one marble from Urn 1 and
puts it into Urn 2. Then Rob picks one marble from Urn 2. If the marble
picked from Urn 2 is red, what is the probability that the marble picked from
Urn 1 was also red?
Section 8-5
Ex 1. Rob has 6 bills in his wallet: 3 ones, 2 fives, and a twenty. He randomly
picks 2 bills from his wallet. Define a random variable for this experiment
Ex 2. Find the probability distribution for the random variable from Ex 1.
Ex 3. Find the expected value of the random variable from Ex 2.