13.1 Theoretical Probability Solution Key
An integer from 1 to 40 is drawn at random. Find the probability that it is
1. odd.
There are 20 odd numbers from 1 to 40: {1, 3, 5, 7, 9, 11, 13, 15, ..., 33, 35, 37, 39}. So the probability
20 1
that an odd number will be chosen is P odd = = .
40 2
2. even.
There are 20 even numbers from 1 to 40: {2, 4, 6, 8, 10, 12, 14, ..., 36, 38, 40}. So the probability that
20 1
an even number will be chosen is P even = = .
40 2
3. a multiple of 4.
The multiples of 4 from 1 to 40 are {4, 8, 12, 16, 20, 24, 28, 32, 36, 40}. There are 10 of them, so the
10 1
probability that one will be chosen is P  multiple of 4= = .
40 4
4. prime
A prime number is a positive whole number which has exactly two divisors: 1 and itself. The primes
from 1 to 40 are {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}. There are 12 of them, so the probability that
12 3
one will be chosen is P  prime= =
.
40 10
5. odd and a multiple of 5.
The odd numbers: {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39}.
The multiples of 5: {5, 10, 15, 20, 25, 30, 35, 40}.
The numbers which are odd and multiples of 5 are the numbers which are in both sets: {5, 15, 25, 35}.
4
1
Since there are 4, P odd and multiple of 5 = =
.
40 10
6. odd or a multiple of 5.
The numbers which are odd or multiples of 5 are the numbers which are in either or both sets: {1, 3, 5,
7, 9, 10, 11, 13, 15, 17, 19, 20, 21, 23, 25, 27, 29, 30, 31, 33, 35, 37, 39, 40}. Since there are 24,
24 3
P odd or multiple of 5= = .
40 5
Advanced Math Topics
p. 1
Monday, December 3, 2007
The letters in the word constitution are written on index cards and placed
in a brown bag.
7. A letter is selected at random. Find the probability that it is a vowel.
In the word C O N S T I T U T I O N (12 letters) the vowels (AEIOUY) are: C O N S T I T U T I O N.
5
There are 5 vowels in this 12-letter word, so the probability is P  vowel=
.
12
8. What is the probability of selecting the letter T?
Where are the T's? C O N S T I T U T I O N. There are 3 T's in this 12-letter word, so the probability
3 1
is P T= = .
12 4
9. What is the probability of selecting a consonant?
Where are the consonants? C O N S T I T U T I O N. There are 7 consonants in this 12-letter word,
7
so the probability is P consonants=
.
12
States of the Union
10. Find the probability that the name of a state chosen
at random begins with the letter N.
The map on the page lists 8 states whose name begin with
the letter N. The United States has 50 states; so the
8
4
probability is P state starting with N= =
.
50 25
11. Find the probability that the name of a state chosen at random begins with the letter B.
There are no states whose names begin with the letter B. So the probability of picking one is
0
P state starting with B= =0 .
50
Advanced Math Topics
p. 2
Monday, December 3, 2007
A student who was surveyed is chosen at
random. What is the theoretical
probability that the student
12. is a girl?
There are 29 girls out of the 59 students, so the probability is P girl =
29
.
59
13. liked the lunch drink?
35 students liked the lunch drink, so the probability is P liked the drink=
35
.
59
14. is a girl and liked the lunch drink?
There are 19 girls who liked the drink, so the probability is P girl and liked the drink =
19
.
59
15. is a girl or liked the lunch drink?
There are 161910=45 students who are girls or
liked the lunch drink. So the probability is
45 .
P girl or liked the drink =
59
Advanced Math Topics
p. 3
Monday, December 3, 2007