7th Grade Common Core Math Worksheets - Free Printable

Let’s solve each problem one by one, step by step.

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Problem 1:
Six balls numbered from 1 to 6 are placed in an urn. If one ball is selected at random, find the probability that it is an odd-numbered ball.

Step 1: List all possible outcomes → {1, 2, 3, 4, 5, 6} → total = 6

Step 2: Find which numbers are odd → {1, 3, 5} → count = 3

Step 3: Probability = favorable / total = 3/6 = 1/2

✔ Final Answer for Problem 1: [B] 1/2

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Problem 2:
A single six-sided fair die is tossed. Find the probability of obtaining a number greater than 4.

Step 1: Possible outcomes → {1, 2, 3, 4, 5, 6} → total = 6

Step 2: Numbers greater than 4 → {5, 6} → count = 2

Step 3: Probability = 2/6 = 1/3

✔ Final Answer for Problem 2: [A] 1/3

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Problem 3:
You are one of 30 people entering a contest. What is the probability that your name will be drawn first?

Step 1: Total people = 30

Step 2: Only 1 person wins (you) → favorable = 1

Step 3: Probability = 1/30

✔ Final Answer for Problem 3: [C] 1/30

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Problem 4:
Given the set of numbers {0, 1, 2, 3, 4, 5, 6, 7, 8}, if one of the numbers is chosen at random, find the probability that the number is a solution of 3x + 1 < 13.

Step 1: Solve inequality:
3x + 1 < 13
→ 3x < 12
→ x < 4

Step 2: From the set {0,1,2,3,4,5,6,7,8}, which numbers are less than 4?
→ {0, 1, 2, 3} → count = 4

Step 3: Total numbers in set = 9

Step 4: Probability = 4/9

✔ Final Answer for Problem 4: [B] 4/9

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Problem 5:
What is the probability of drawing a spade from a deck of 52 playing cards?

Step 1: A standard deck has 52 cards.

Step 2: There are 4 suits: hearts, diamonds, clubs, spades → each suit has 13 cards.

So, spades = 13 cards.

Step 3: Probability = 13/52 = 1/4

✔ Final Answer for Problem 5: [D] 1/4

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Problem 6:
Spinner with sections: 64, 24, 22, 54, 36, 18, 10, 12 → total 8 equal sections.

We need probability that spinner lands on a multiple of both 3 and 4.

Note: Multiple of both 3 and 4 → must be multiple of LCM(3,4) = 12.

Check each number:

- 64 ÷ 12 = 5.33… → no
- 24 ÷ 12 = 2 → yes ✔
- 22 ÷ 12 ≈ 1.83 → no
- 54 ÷ 12 = 4.5 → no
- 36 ÷ 12 = 3 → yes ✔
- 18 ÷ 12 = 1.5 → no
- 10 ÷ 12 ≈ 0.83 → no
- 12 ÷ 12 = 1 → yes ✔

Favorable outcomes: 24, 36, 12 → count = 3

Total sections = 8

Probability = 3/8

✔ Final Answer for Problem 6: [C] 3/8

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Problem 7:
Joseph has:
- 2 pairs white socks → 4 individual white socks
- 4 pairs black socks → 8 individual black socks
- 1 pair blue socks → 2 individual blue socks

Total socks = 4 + 8 + 2 = 14

He picks ONE sock at random. We want probability it’s black.

Black socks = 8

Probability = 8/14 = 4/7

✔ Final Answer for Problem 7: [C] 4/7

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Final Answer:
1. [B]
2. [A]
3. [C]
4. [B]
5. [D]
6. [C]
7. [C]