Sure! Let’s solve each problem step by step. We are choosing a number
at random from 1 to 10, so the total number of possible outcomes is
10.
---
1) Probability of selecting a multiple of 2
Multiples of 2 between 1 and 10:
→ 2, 4, 6, 8, 10 →
5 numbers
Probability = favorable outcomes / total outcomes =
5/10 = 1/2
✔ Answer: 1/2
---
2) Probability of selecting a multiple of 3
Multiples of 3 between 1 and 10:
→ 3, 6, 9 →
3 numbers
Probability =
3/10
✔ Answer: 3/10
---
3) Probability of selecting an odd number
Odd numbers between 1 and 10:
→ 1, 3, 5, 7, 9 →
5 numbers
Probability =
5/10 = 1/2
✔ Answer: 1/2
---
4) Probability of NOT selecting a multiple of 2
From #1, probability of selecting a multiple of 2 is 5/10 = 1/2
So, probability of
not selecting one = 1 - 1/2 =
1/2
Alternatively, non-multiples of 2 are the odd numbers (same as #3): 1,3,5,7,9 → 5 numbers → 5/10 = 1/2
✔ Answer: 1/2
---
5) Probability of NOT selecting a multiple of 3
From #2, probability of selecting a multiple of 3 is 3/10
So, probability of
not selecting one = 1 - 3/10 =
7/10
Non-multiples of 3: 1,2,4,5,7,8,10 → 7 numbers → 7/10
✔ Answer: 7/10
---
6) Probability of NOT selecting a multiple of 2 OR a multiple of 3
This means we want numbers that are
neither multiples of 2
nor multiples of 3.
First, list all numbers from 1 to 10:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Multiples of 2: 2,4,6,8,10
Multiples of 3: 3,6,9
→ Union (multiples of 2 or 3): 2,3,4,6,8,9,10 →
7 numbers
So, numbers that are
NOT multiples of 2 or 3:
→ 1, 5, 7 →
3 numbers
Probability =
3/10
✔ Answer: 3/10
---
7) Probability of selecting a multiple of 2 OR a multiple of 3
From above (#6), we found that there are
7 numbers that are multiples of 2 or 3:
2,3,4,6,8,9,10
Probability =
7/10
✔ Answer: 7/10
*(Note: This is the complement of #6)*
---
8) Probability of selecting a 3 or smaller
Numbers ≤ 3: 1, 2, 3 →
3 numbers
Probability =
3/10
✔ Answer: 3/10
---
9) Probability of selecting a 8 or greater
Numbers ≥ 8: 8, 9, 10 →
3 numbers
Probability =
3/10
✔ Answer: 3/10
---
10) Probability of selecting factors of 4 AND factors of 6
We need numbers that are
common factors of both 4 and 6 — i.e.,
factors of GCF(4,6).
Factors of 4: 1, 2, 4
Factors of 6: 1, 2, 3, 6
→ Common factors:
1, 2
So, numbers from 1 to 10 that are factors of both 4 and 6:
1 and 2
→
2 numbers
Probability =
2/10 = 1/5
✔ Answer: 1/5
---
##
✔ Final Answers:
1)
1/2
2)
3/10
3)
1/2
4)
1/2
5)
7/10
6)
3/10
7)
7/10
8)
3/10
9)
3/10
10)
1/5
Let me know if you’d like these explained in a different way or with diagrams!
Parent Tip: Review the logic above to help your child master the concept of 6th grade math probability worksheet.
