Let’s solve each problem one by one, step by step.
---
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 are odd → {1, 3, 5} → count = 3
Step 3: Probability = favorable / total = 3/6 = 1/2
✔ Final Answer for #1: [B] 1/2
---
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 > 4 → {5, 6} → count = 2
Step 3: Probability = 2/6 = 1/3
✔ Final Answer for #2: [A] 1/3
---
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 #3: [C] 1/30
---
Problem 4:
Given the set of numbers {0, 1, 2, 3, 4, 5, 6, 7, 8}, if one number is chosen at random, find the probability that it is a solution of 3x + 1 < 13.
Step 1: Solve inequality:
3x + 1 < 13
→ 3x < 12
→ x < 4
Step 2: Which numbers in the set 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 #4: [B] 4/9
---
Problem 5:
What is the probability of drawing a spade from a deck of 52 playing cards?
Step 1: A standard deck has 4 suits: hearts, diamonds, clubs, spades → each suit has 13 cards.
Step 2: Spades = 13 cards
Step 3: Probability = 13/52 = 1/4
✔ Final Answer for #5: [D] 1/4
---
Problem 6:
Spinner with sections: 64, 24, 22, 54, 36, 18, 10, 12 → total 8 equal sections.
We want 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
✔
So multiples of 12: 24, 36, 12 → 3 numbers
Total sections = 8
Probability = 3/8
✔ Final Answer for #6: [C] 3/8
---
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 #7: [C] 4/7
---
Final Answer:
1. [B]
2. [A]
3. [C]
4. [B]
5. [D]
6. [C]
7. [C]
Parent Tip: Review the logic above to help your child master the concept of probability worksheet 7th grade math.
