M
Math Coach Amy
Amy Ferguson Moncure

7th Grade Math ยท Unit 7

Theoretical
Probability

Theoretical probability compares favorable outcomes with equally likely outcomes.

Jump to section:

Key Ideas Easy Medium Hard
What to Remember

Favorable over possible

Theoretical probability is favorable outcomes over equally likely outcomes.

Simplify

Simplify the fraction.

Level 1

Easy

Coins, dice, and spinners

Example
Find the theoretical probability of flipping heads on a coin.

probability = favorable outcomespossible outcomes

probability = 12

Answer: 12

1
Find the theoretical probability of flipping tails on a coin.
Show Answer

probability = favorable outcomespossible outcomes

probability = 12

Answer: 12

2
Find the theoretical probability of rolling a 1 on a die.
Show Answer

probability = favorable outcomespossible outcomes

probability = 16

Answer: 16

3
Find the theoretical probability of rolling a 3 on a die.
Show Answer

probability = favorable outcomespossible outcomes

probability = 16

Answer: 16

4
Find the theoretical probability of rolling a 5 on a die.
Show Answer

probability = favorable outcomespossible outcomes

probability = 16

Answer: 16

5
Find the theoretical probability of landing on section 1 of an 8 section spinner.
Show Answer

probability = favorable outcomespossible outcomes

probability = 18

Answer: 18

6
Find the theoretical probability of landing on section 4 of an 8 section spinner.
Show Answer

probability = favorable outcomespossible outcomes

probability = 18

Answer: 18

7
Find the theoretical probability of landing on section 8 of an 8 section spinner.
Show Answer

probability = favorable outcomespossible outcomes

probability = 18

Answer: 18

8
Find the theoretical probability of landing on section 2 of a 10 section spinner.
Show Answer

probability = favorable outcomespossible outcomes

probability = 110

Answer: 110

9
Find the theoretical probability of landing on section 6 of a 10 section spinner.
Show Answer

probability = favorable outcomespossible outcomes

probability = 110

Answer: 110

10
Find the theoretical probability of landing on section 10 of a 10 section spinner.
Show Answer

probability = favorable outcomespossible outcomes

probability = 110

Answer: 110

Level 2

Medium

A fraction to simplify

Example
Find the theoretical probability of rolling an even number on a die.

probability = favorable outcomespossible outcomes

probability = 36

12

Answer: 12

1
Find the theoretical probability of rolling an odd number on a die.
Show Answer

probability = favorable outcomespossible outcomes

probability = 36

12

Answer: 12

2
Find the theoretical probability of rolling a number greater than 4 on a die.
Show Answer

probability = favorable outcomespossible outcomes

probability = 26

13

Answer: 13

3
Find the theoretical probability of rolling a number greater than 2 on a die.
Show Answer

probability = favorable outcomespossible outcomes

probability = 46

23

Answer: 23

4
Find the theoretical probability of landing on red when 2 of 8 spinner sections are red.
Show Answer

probability = favorable outcomespossible outcomes

probability = 28

14

Answer: 14

5
Find the theoretical probability of landing on blue when 4 of 8 spinner sections are blue.
Show Answer

probability = favorable outcomespossible outcomes

probability = 48

12

Answer: 12

6
Find the theoretical probability of landing on green when 6 of 8 spinner sections are green.
Show Answer

probability = favorable outcomespossible outcomes

probability = 68

34

Answer: 34

7
Find the theoretical probability of landing on yellow when 2 of 10 spinner sections are yellow.
Show Answer

probability = favorable outcomespossible outcomes

probability = 210

15

Answer: 15

8
Find the theoretical probability of landing on purple when 4 of 10 spinner sections are purple.
Show Answer

probability = favorable outcomespossible outcomes

probability = 410

25

Answer: 25

9
Find the theoretical probability of landing on orange when 5 of 10 spinner sections are orange.
Show Answer

probability = favorable outcomespossible outcomes

probability = 510

12

Answer: 12

10
Find the theoretical probability of landing on pink when 8 of 10 spinner sections are pink.
Show Answer

probability = favorable outcomespossible outcomes

probability = 810

45

Answer: 45

Level 3

Hard

Counts in the sentence

Example
Find the theoretical probability of drawing a red marble when 3 of 12 marbles are red.

probability = favorable outcomespossible outcomes

probability = 312

14

Answer: 14

1
Find the theoretical probability of drawing a blue marble when 5 of 15 marbles are blue.
Show Answer

probability = favorable outcomespossible outcomes

probability = 515

13

Answer: 13

2
Find the theoretical probability of drawing a green marble when 4 of 16 marbles are green.
Show Answer

probability = favorable outcomespossible outcomes

probability = 416

14

Answer: 14

3
Find the theoretical probability of drawing a yellow marble when 6 of 18 marbles are yellow.
Show Answer

probability = favorable outcomespossible outcomes

probability = 618

13

Answer: 13

4
Find the theoretical probability of drawing a black card when 8 of 20 cards are black.
Show Answer

probability = favorable outcomespossible outcomes

probability = 820

25

Answer: 25

5
Find the theoretical probability of drawing a heart when 13 of 52 cards are hearts.
Show Answer

probability = favorable outcomespossible outcomes

probability = 1352

14

Answer: 14

6
Find the theoretical probability of picking a winning ticket when 2 of 14 tickets win.
Show Answer

probability = favorable outcomespossible outcomes

probability = 214

17

Answer: 17

7
Find the theoretical probability of selecting a ripe apple when 9 of 21 apples are ripe.
Show Answer

probability = favorable outcomespossible outcomes

probability = 921

37

Answer: 37

8
Find the theoretical probability of choosing a mystery novel when 7 of 28 books are mystery novels.
Show Answer

probability = favorable outcomespossible outcomes

probability = 728

14

Answer: 14

9
Find the theoretical probability of spinning red when 9 of 24 sections are red.
Show Answer

probability = favorable outcomespossible outcomes

probability = 924

38

Answer: 38

10
Find the theoretical probability of pulling a striped sock when 8 of 32 socks are striped.
Show Answer

probability = favorable outcomespossible outcomes

probability = 832

14

Answer: 14

Need help with this skill?

Book a Session with Amy