Spring 2016 Math 166
2
Week in Review II
Section 1.3
1. A fair 6-sided die has 3 sides painted
red, 2 sides painted blue, and 1 side
courtesy: David J. Manuel
painted white.
The die is rolled and
the color of the top side is observed.
(covering Sections 1.2-1.4)
What is the sample space?
Are the
outcomes equally likely?
1
2. A card is drawn from a standard 52-
Section 1.2
card deck and its color is recorded.
If the card is black, a coin is tossed
n(A) = 60, n(B) = 80, and
n(A ∩ B) = 50, what is n(A ∪ B)?
1. Given
and the upward face (heads or tails) is
recorded.
n(A) = 40, n(B) = 100,
n(A ∪ B) = 130, and n(U ) = 200:
2. Given
(a) What is
n(A ∩ B)?
(b) What is
n(Ac ∩ B c )?
tom number is recorded.
(a) What is the sample space? Are the outcomes equally likely?
(b) List the outcomes in the event A red
n(U ) = 400, n(A) = 180,
n(B) = 230, n(C) = 170, n(A ∩ B) =
120, n(A ∩ C) = 70, n(B ∩ C) = 50,
c
and n(A ∩ B ∩ C ) = 80, nd the fol-
3. Given
card is drawn.
3. A
n(A ∩ B ∩ C)
(b)
n(A ∩ B c ∩ C c )
(c)
n(A ∪ B ∪ C)
letter is chosen at random from
FIGHTIN TEXAS AGGIES (ignore
lowing:
(a)
If the card is red, a fair 4-
sided die (#1-4) is tossed and the bot-
spaces).
Let
be the event that a
F
be the event
that one of the rst six letters of the
alphabet is chosen. List the outcomes
in each of the following:
4. A social media survey of 200 teenagers
(a)
E∪F
gathered the following information:
(b)
Ec ∩ F
(c)
Ec ∪ F c
•
E
vowel is chosen and
72 had a Snapchat account but not a
Tumblr account
•
4. A digit (0-9) is chosen at random. Let
25 had a Tumblr account but not a
E
Snapchat account
•
5 had only a Kik account
•
50 had a Kik and Snapchat account
•
20 had all three accounts
•
167 had a Snapchat or Tumblr account
be the event that the digit is a prime
number,
F
be the event that the digit
is greater than 5, and
G
be the event
that the digit is less than 4. List the
outcomes in each of the following:
(a) How many did not have any of these accounts?
(b) How many had only a Snapchat account?
1
(a)
E∪F ∪G
(b)
E c ∪ F c ∪ Gc
(c)
E∩F ∩G
(d)
Ec ∪ F ∪ G
3
Section 1.4
1. Find the probabilities of each of the
events in #1 and #4 of the previous
section
2. A fair 6-sided die (#1-6) and a fair 4-
sided die (#1-4) are tossed:
(a) What is the probability that the sum of
the numbers is at least 7?
(b) What is the probability that the difference between the larger and smaller
number is at least 2?
(c) What is the probability that a 2 is rolled
or the sum is at least 7?
3. The
results
of
a
(made-up)
Texas
A&M survey of 500 students on political party preference are given below:
Choice
Republican
Democrat
Other
# selected
355
120
18
Political Parties are evil
and must be abolished
7
What is the empirical probability that
a survey taker chosen at random:
(a) Is Republican?
(b) Is neither Republican nor Democrat?
2