Properties of Probability Exercise
1. For each of the following experiments,
(i) suggest a set of possible outcomes;
(ii) decide whether the outcomes are equally likely.
(a) Spinning a roulette wheel
(b) Throwing a dart at a dart board
(c) Choosing a job applicant for a position of employment from ten
applicants whom you have interviewed
(d) Selecting a dress from a rack of dresses
(e) Spinning a racquet to determine “rough” or “smooth” in order to start
a game
(f) Selecting the winner of a lottery
(g) Playing a game of bingo. Bingo is a game of chance played with
different randomly drawn numbers which players match against
numbers that have been pre-printed on 5×5 cards. A typical Bingo game
utilizes the numbers 1 through 75.
2. (a) Given: S = {1, 3, 5, 7, 9}
A = {3, 9}
Find: P (A)
(b) Given: S = {HH, HT, TH, TT}
A = {HT, TH}
Find: P (A)
(c) Given: S = {a, b, c, d, e, f, …, w, x, y, z}
A = {a, e, i, o, u}
Find: P (A), P (𝐴’)
3. (a) Given: Experiment: rolling a die.
Event: an odd number turns up.
Find: the probability of rolling an odd number with a die.
(b) Given: Experiment: choosing a number at random from 1 to 100
inclusive.
Event: the number is divisible by 3.
Find: the probability that a number chosen at random between 1
and 100 is not divisible by 3.
(b) Given: Experiment: cutting a deck of cards.
Event: the card cut is a face card.
Find: the probability of cutting a face card from a deck of cards.
4. The game “Dungeons and Dragons” is played with a dodecahedral
die, that is, a die with twelve faces. What is the probability of rolling a
number greater than 7?
5. A record collection consists of 8 rock albums, twelve blues albums,
and 4 classical albums. If a record is chosen at random find the
probability that the one chosen is
(a) rock
(b) classical
(c) blues
(d) not classical
(e) neither blues nor classical
6. An integer from 1 to 50 is chosen at random. What is the probability
that the integer
(a) is odd?
(b) is even?
(c) is less tan nine?
(d) is divisible by 11?
(e) ends in a 7?
(f) is a perfect cube?
(g) is not a perfect square?
(h) is not divisible by 7?
(i) is not a multiple of 5?
7. A drawer contains 3 pairs of red socks, 2 pairs of white socks, and 4
pairs of black socks and the socks are not matched or organized in any
special way.
(a) If the lights are out, and one sock is drawn from the drawer, what is
the probability that a red sock is drawn?
(b) Once a sock has been drawn and discovered to be red, what is the
probability of drawing another red sock to make a pair?
8. Three downhill skiers, Lawrie, Gavin, and Alan are competing in a
race. Their positions in the starting order are chosen by lot, that is
randomly. What is the probability that
(a) Gavin races before Lawrie?
(b) Alan is the last racer?
(c) Lawrie races first?
(d) Gavin follows immediately after Alan?
9. Find the probability that a number chosen at random between 1 and
100 inclusive is:
(a) Divisible by 3 and 5
(b) Divisible by 3 or 5
(c) Not divisible by 3 and 5
(d) Not divisible by 3 or 5
ANSWERS
1. (a) {00, 0, 1, 2, 3, …, 3, 36}. Yes.
(b) {1, 2, …, 20}. Yes.
(c) {applicant #1, applicant #2, …, applicant #10}. No.
(d) {polka dots, striped, plain}. No.
(e) {rough, smooth}. Yes.
(f) {ticket #1, ticket #2, …, ticket # n} Yes.
(g) {1, 2, …, 75}. Yes.
2. (a)
3. (a)
4.
2
5
1
2
(b)
1
(c)
2
67
(b)
100
5 21
,
26 26
(c)
3
13
5
12
1
1
1
5
3
6
2
6
5. (a) (b) (c) (d)
6. (a)
7. (a)
8. (a)
9. (a)
1
2
1
3
1
2
3
50
1
(b)
2
(b)
(b)
1
3
(b)
4
(c)
25
(e)
(d)
1
3
2
25
(e)
1
10
5
17
(c)
47
100
1
3
(d)
(c)
1
3
53
100
(d)
47
50
(f)
3
50
(g)
43
50
(h)
43
50
(i)
4
5