Math 110 Review for Exam 2 Spring 2002
1. Three coins are tossed. Using ordered triples, give: (a) the sample space,
(b) the event E that at least two are heads, (c) the probability that at least two are heads.
2. A family has 3 children. Using gto stand for girl and bfor boy, and using ordered
triples such as (b, g, g), find (a) the sample space (list all elements), (b) the event Ethat the
family has exactly two daughters, (c) p(E) and o(E).
3. If p(E) = 5
9,p(F0) = 3
9and p(E∪F) = 8
9,
(a) find p(F), (b) find p(E∩F), (c) and find o(E∪F).
4. A 6/47 lottery requires choosing six of the numbers between 1 and 47. (a) How
many different lottery tickets can you choose? (b) What is the probability of having at least
one winning number?
5. (20 pts) A pair of dice is rolled. Using ordered pairs, list the elements of the fol-
lowing: (a) The event Ethat the sum is 6. (b) Find probability that the sum is 6. (c) The
event Fthat the difference is 2. (d) Find probability that the sum equals 6 or the difference
is 2.
6. The Department of Mathematics at the University of Southwestern North Dakota
consists of 19 full-time faculty members. 14 are men and 5 are women. A four-person hiring
committee must be selected by the chair. How many committees are possible if it must con-
sist of the following? (a) Two women and two men. (b) Any mixture of men and women.
(c) At least one woman.
7. From a standard deck with 52 cards your are being dealt a hand consisting of 5 cards.
(a) How many different hands with exactly 4 spades are possible? (b) How many different
hands with 5 hearts are possible? What is the probability of being dealt 5 hearts? (c) How
many different hands in one suit are possible? What is the probability of being dealt a hand
consisting of cards in one suit? (d) How many hands with 2 hearts and 3 spades are possible?
What is the probability of being dealt 2 hearts and 3 spades? (e) What is the probability of
being dealt a hand with no hearts at all? (f ) What is the probability of being dealt a hand
with at least one king?
8. Find the expected value of a $1 bet in the following game: You are being dealt one
card from a deck of 54 cards (standard 52-card deck plus two jokers). If your card is a di-
amond you win $3. Otherwise you lose the bet. Would you play this game? Why or why not?
9. Find the expected value of a $1 bet in the following game:
A pair of dice is rolled. If the sum equals 8, the player wins $6. Otherwise the player loses
the bet. Would you play this game? Why or why not?
Additional Problems:
Section 2.4,Problems 18, 21, 23, 25, 29, 33
Section 3.2,Problems 27, 49, 51, 55,
Section 3.3,Problems 13, 27, 29, 39–42, 51, 53
Section 3.4,Problems 7, 15, 17–25
Section 3.5,Problems 3, 9, 21, 23, 27, 29