Let’s solve each problem step by step with clear explanations.
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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.
Solution:
- Total possible outcomes = 6 (balls numbered 1 through 6)
- Odd-numbered balls: 1, 3, 5 →
3 favorable outcomes
- Probability = Favorable / Total = 3/6 =
1/2
✔ Answer: [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.
Solution:
- Die faces: 1, 2, 3, 4, 5, 6 → total 6 outcomes
- Numbers > 4: 5 and 6 →
2 favorable outcomes
- Probability = 2/6 =
1/3
✔ Answer: [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?
Solution:
- All 30 people have equal chance to be drawn first.
- Only 1 favorable outcome (your name)
- Probability = 1/30
✔ Answer: [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.
Solution:
First, solve the inequality:
> 3x + 1 < 13
> Subtract 1: 3x < 12
> Divide by 3: x < 4
So, we want numbers in the set {0,1,2,3,4,5,6,7,8} that are
less than 4.
That’s: 0, 1, 2, 3 →
4 favorable outcomes
Total numbers in set = 9
Probability = 4/9
✔ Answer: [B] 4/9
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Problem 5:
> What is the probability of drawing a spade from a deck of 52 playing cards?
Solution:
- Standard deck has 52 cards
- 4 suits: hearts, diamonds, clubs, spades → each suit has 13 cards
- So, spades = 13 cards
Probability = 13/52 =
1/4
✔ Answer: [D] 1/4
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Problem 6:
> This is a spinner used in a board game Helen invented.
> Spinner has 8 sections: 64, 24, 22, 54, 36, 18, 10, 12
> What is the probability that the spinner will land on a multiple of 3 and 4?
Solution:
We need numbers that are multiples of
both 3 and 4, i.e., multiples of
LCM(3,4) = 12.
Check each number:
- 64 → 64 ÷ 12 = 5.33 → not divisible by 12
- 24 → 24 ÷ 12 = 2 →
✔ YES
- 22 → 22 ÷ 12 ≈ 1.83 → NO
- 54 → 54 ÷ 12 = 4.5 → NO
- 36 → 36 ÷ 12 = 3 →
✔ YES
- 18 → 18 ÷ 12 = 1.5 → NO
- 10 → 10 ÷ 12 ≈ 0.83 → NO
- 12 → 12 ÷ 12 = 1 →
✔ YES
Favorable outcomes: 24, 36, 12 →
3 numbers
Total sections = 8
Probability = 3/8
✔ Answer: [C] 3/8
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Problem 7:
> Donato’s little brother Joseph is too small to see inside his sock drawer. Joseph has 2 pairs of white socks, 4 pairs of black socks, and 1 pair of blue socks inside his drawer. If the socks are not paired together, what is the probability that Joseph will reach inside his drawer and pick a black sock?
Solution:
Note: “Pairs” means 2 socks per pair.
- White socks: 2 pairs = 4 socks
- Black socks: 4 pairs = 8 socks
- Blue socks: 1 pair = 2 socks
Total socks = 4 + 8 + 2 =
14 socks
Black socks = 8
Probability of picking a black sock = 8/14 =
4/7
✔ Answer: [C] 4/7
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✔ Final Answers:
1.
[B] 1/2
2.
[A] 1/3
3.
[C] 1/30
4.
[B] 4/9
5.
[D] 1/4
6.
[C] 3/8
7.
[C] 4/7
Let me know if you’d like visual diagrams or further clarification!
Parent Tip: Review the logic above to help your child master the concept of 7th grade math worksheet common core.
