MATH 110 Sec 13.1 Intro to Probability Practice Exercises
We are flipping 3 coins and the outcomes are represented by a string of H’s and T’s (HTH, etc.).
How many elements are there in the sample space?
Express the event “There are more heads than tails” as a set.
What is the probability that there are more heads than tails?

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
We are flipping 3 coins and the outcomes are represented by a string of H’s and T’s (HTH, etc.).
How many elements are there in the sample space?
By the Fundamental Counting Principle: 2 x 2 x 2 = 8
Express the event “There are more heads than tails” as a set.
{ HHH , HHT , HTH , THH }
What is the probability that there are more heads than tails?
By the Basic Probability Principle,
# 𝑤𝑎𝑦𝑠 𝑡𝑜 𝑔𝑒𝑡 𝑚𝑜𝑟𝑒 𝐻𝑒𝑎𝑑𝑠
𝑃 𝑚𝑜𝑟𝑒 𝐻 𝑡ℎ𝑎𝑛 𝑇 =
# 𝑜𝑓 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑠 𝑖𝑛 𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑝𝑎𝑐𝑒
=
4
8
=
1
2

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
Four cards are drawn from a well-shuffled 52-card deck.
What is the probability of drawing a heart?

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
Four cards are drawn from a well-shuffled 52-card deck.
What is the probability of drawing a heart?
4 suits (CLUBS, SPADES,
𝑃 𝐻𝑒𝑎𝑟𝑡 =
13
)
52
=
1
4
13 CLUBS
13 SPADES
13 HEARTS
13 DIAMONDS

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
Four cards are drawn from a well-shuffled 52-card deck.
What are the odds against drawing a heart?
Notice that there are 13 Hearts and 39 non-Hearts
Odds against drawing Heart are 39 : 13 which reduces to 3 : 1.

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
Four cards are drawn from a well-shuffled 52-card deck.
What is the probability that all 4 are black?

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
Four cards are drawn from a well-shuffled 52-card deck.
What is the probability that all 4 are black?
What is the probability that all 4 are black?
26 black cards
26 red cards

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
Four cards are drawn from a well-shuffled 52-card deck.
What is the probability that all 4 are black?
From previous picture, there are
26 black cards and 52 cards in all.
Because the order the cards are drawn is not important, we count the cards using combinations.
There are 𝐶 26,4 = 14950 ways to choose 4 black cards.
There are 𝐶 52,4 = 270725 ways to choose any 4 cards.
By the Basic Probability Principle,
# 𝑜𝑓 𝑤𝑎𝑦𝑠 𝑡𝑜 𝑐ℎ𝑜𝑜𝑠𝑒 4 𝑏𝑙𝑎𝑐𝑘
𝑃 𝑎𝑙𝑙 4 𝑏𝑙𝑎𝑐𝑘 =
# 𝑜𝑓 𝑤𝑎𝑦𝑠 𝑡𝑜 𝑐ℎ𝑜𝑜𝑠𝑒 𝑎𝑛𝑦 4 𝑐𝑎𝑟𝑑𝑠
=
𝐶(26,4)
𝐶(52,4)
14950
=
270725
46
=
833

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
Support Oppose
Opinions of residents in a town and surrounding area about a proposed racetrack is given here.
Live in town
Live in area surrounding
3325 392
4747 617
A reporter randomly selects one of these 9081 people to interview.
What is the probability that the person is for the track?
What are the odds against the person supporting the track?

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
Support Oppose
Opinions of residents in a town and surrounding area about a proposed racetrack is given here.
Live in town
Live in area surrounding
3325 392
4747 617
A reporter randomly selects one of these 9081 people to interview.
What is the probability that the person is for the track?
𝑃 𝑆𝑢𝑝𝑝𝑜𝑟𝑡𝑠 𝑡𝑟𝑎𝑐𝑘 =
3325 + 4747
9081
=
8072
9081
=
2 × 2 × 2 × 1009
3 × 3 × 1009
What are the odds against the person supporting the track?
=
8
9
1 : 8

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
If a dart is thrown and hits somewhere in the diagram below, what is the probability that it hits the shaded area?
(Write final answer as a decimal rounded to 4 decimal places.)
8 in.
6 in.
4 in.
4 in.
3 in.
2 in.
2 in.
1 in.

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
If a dart is thrown and hits somewhere in the diagram below, what is the probability that it hits the shaded area?
(Write final answer as a decimal rounded to 4 decimal places.)
Note: The probability of hitting a region is proportional to the area of that region and the whole diagram.
2 in.
2
4 in.
1
1 in.
𝑠ℎ𝑎𝑑𝑒𝑑 𝑎𝑟𝑒𝑎
𝑃 ℎ𝑖𝑡 𝑠ℎ𝑎𝑑𝑒𝑑 𝑎𝑟𝑒𝑎 = 𝑡𝑜𝑡𝑎𝑙 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑑𝑖𝑎𝑔𝑟𝑎𝑚
=
6 in.
2
8 in.
2 in.
3 in.
4 in.
2 × 1 + (2 × 2)
=
8 × 4
2 + 4
=
32
6
32
= 0.1875

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
If a dart is thrown and hits somewhere in the figure below which is built from 4 different size squares (2 blue and 2 green), what is the probability that it hits the green area?
(Write final answer as an integer or simplified fraction.)
21 in.
9 in.
6 in.
15 in.

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
If a dart is thrown and hits somewhere in the figure below which is built from 4 different size squares (2 blue and 2 green), what is the probability that it hits the green area?
(Write final answer as an integer or simplified fraction.)
Note: The probability of hitting a region is proportional to the area of that region and the whole diagram.
21 in.
9 in.
6 in.
15 in.

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
If a dart is thrown and hits somewhere in the figure below which is built from 4 different size squares (2 blue and 2 green), what is the probability that it hits the green area?
(Write final answer as an integer or simplified fraction.)
Note: The probability of hitting a region is proportional to the area of that region and the whole diagram.
Area of the biggest green square is
15 x 15 = 225
15 in.
225
21 in.
9 in.
6 in.
15 in.

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
If a dart is thrown and hits somewhere in the figure below which is built from 4 different size squares (2 blue and 2 green), what is the probability that it hits the green area?
(Write final answer as an integer or simplified fraction.)
Note: The probability of hitting a region is proportional to the area of that region and the whole diagram.
Area of the biggest green square is
15 x 15 = 225
15 in.
9 in.
Area of
Small blue square is
9 x 9 =81
225
Subtract blue area b/c it covers up part of the green.
- 81
144
21 in.
9 in.
6 in.
15 in.

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
If a dart is thrown and hits somewhere in the figure below which is built from 4 different size squares (2 blue and 2 green), what is the probability that it hits the green area?
(Write final answer as an integer or simplified fraction.)
Note: The probability of hitting a region is proportional to the area of that region and the whole diagram.
Area of the biggest green square is
15 x 15 = 225
15 in.
9 in.
Area of
Small blue square is
9 x 9 =81
225
Subtract blue area b/c it covers up part of the green.
- 81
144
36
+ 36
6 in.
The small green square sits on the small blue square and adds back more green.
144 + 36 = 180
21 in.
9 in.
6 in.
15 in.

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
If a dart is thrown and hits somewhere in the figure below which is built from 4 different size squares (2 blue and 2 green), what is the probability that it hits the green area?
(Write final answer as an integer or simplified fraction.)
21 in.
Note: The probability of hitting a region is proportional to the area of that region and the whole diagram.
Area of the biggest green square is
15 x 15 = 225
15 in.
9 in.
Area of
Small blue square is
9 x 9 =81
225
Subtract blue area b/c it covers up part of the green.
- 81
144
36
+ 36
6 in.
The small green square sits on the small blue square and adds back more green.
144 + 36 = 180
9 in.
6 in.
15 in.

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
If a dart is thrown and hits somewhere in the figure below which is built from 4 different size squares (2 blue and 2 green), what is the probability that it hits the green area?
(Write final answer as an integer or simplified fraction.)
21 in.
Note: The probability of hitting a region is proportional to the area of that region and the whole diagram.
Area of the biggest green square is
15 x 15 = 225
15 in.
9 in.
Area of
Small blue square is
9 x 9 =81
225
Subtract blue area b/c it covers up part of the green.
- 81
144
36
+ 36
6 in.
The small green square sits on the small blue square and adds back more green.
144 + 36 = 180
𝑃 ℎ𝑖𝑡𝑠 𝑔𝑟𝑒𝑒𝑛 =
9 in.
6 in.
15 in.
180
441
=
20
49

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
Player 1 & Player 2 play a ame using
Spinner A and Spinner B as shown.
Player 1 gets to choose one of the spinners, both players spin, and the one getting the larger number wins.
Which spinner should Player 1 choose?
Assuming that choice of spinner what is the probability that Player 1 wins?

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
Player 1 & Player 2 play a ame using
Spinner A and Spinner B as shown.
Player 1 gets to choose one of the spinners, both players spin, and the one getting the larger number wins.
List every possible way the 2 spinners could land, then count the # of times each wins.
Which spinner should Player 1 choose?
Assuming that choice of spinner what is the probability that Player 1 wins?

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
Player 1 & Player 2 play a ame using
Spinner A and Spinner B as shown.
Player 1 gets to choose one of the spinners, both players spin, and the one getting the larger number wins.
List every possible way the 2 spinners could land, then count the # of times each wins.
Which spinner should Player 1 choose?
A spin 1 1 1 4 4 4 9 9 9
B spin 2 7 8 2 7 8 2 7 8
Who wins B B B A B B A A
Assuming that choice of spinner what is the probability that Player 1 wins?
A

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
Player 1 & Player 2 play a ame using
Spinner A and Spinner B as shown.
Player 1 gets to choose one of the spinners, both players spin, and the one getting the larger number wins.
List every possible way the 2 spinners could land, then count the # of times each wins.
Which spinner should Player 1 choose?
B (wins 5 out of 9 times)
A spin 1 1 1 4 4 4 9 9 9
B spin 2 7 8 2 7 8 2 7 8
Who wins B B B A B B A A
Assuming that choice of spinner what is the probability that Player 1 wins?
A

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
Player 1 & Player 2 play a ame using
Spinner A and Spinner B as shown.
Player 1 gets to choose one of the spinners, both players spin, and the one getting the larger number wins.
List every possible way the 2 spinners could land, then count the # of times each wins.
Which spinner should Player 1 choose?
B (wins 5 out of 9 times)
A spin 1 1 1 4 4 4 9 9 9
B spin 2 7 8 2 7 8 2 7 8
Who wins B B B A B B A A
Assuming that choice of spinner what is the probability that Player 1 wins?
𝑃 𝐵 𝑤𝑖𝑛𝑠 =
5
9
A

MATH 110 Sec 13.1 Intro to Probability Practice Exercises
Some more detailed solutions and some more problems and solutions can be found here: http://cas.ua.edu/mtlc/UAMath110/Exercises/Sec13-1ExercisesSOL.pdf