Let’s solve each problem one by one. We’re choosing a number at random from 1 to 10. That means there are 10 possible outcomes:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Probability = (Number of favorable outcomes) ÷ (Total number of outcomes)
Total outcomes = 10
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1) Probability of selecting a multiple of 2
Multiples of 2 between 1 and 10:
→ 2, 4, 6, 8, 10 → that’s
5 numbers
Probability = 5/10 =
1/2
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2) Probability of selecting a multiple of 3
Multiples of 3 between 1 and 10:
→ 3, 6, 9 → that’s
3 numbers
Probability = 3/10
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3) Probability of selecting an odd number
Odd numbers between 1 and 10:
→ 1, 3, 5, 7, 9 → that’s
5 numbers
Probability = 5/10 =
1/2
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4) Probability of NOT selecting a multiple of 2
We already know multiples of 2 are 5 numbers → so NOT multiples of 2 = 10 - 5 =
5 numbers
(These are the odd numbers: 1, 3, 5, 7, 9)
Probability = 5/10 =
1/2
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5) Probability of NOT selecting a multiple of 3
Multiples of 3: 3 numbers → so NOT multiples of 3 = 10 - 3 =
7 numbers
Probability = 7/10
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6) Probability of NOT selecting a multiple of 2 OR a multiple of 3
First, find how many numbers ARE multiples of 2 OR 3.
Multiples of 2: 2, 4, 6, 8, 10 → 5 numbers
Multiples of 3: 3, 6, 9 → 3 numbers
But 6 is in both → don’t count twice!
So total unique numbers that are multiples of 2 or 3:
→ 2, 3, 4, 6, 8, 9, 10 → that’s
7 numbers
Therefore, NOT selecting any of these = 10 - 7 =
3 numbers
Which numbers? Let’s list them:
Numbers from 1 to 10 not divisible by 2 or 3:
→ 1, 5, 7 → yes, 3 numbers
Probability = 3/10
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7) Probability of selecting a multiple of 2 OR a multiple of 3
From above, we found this is
7 numbers: 2, 3, 4, 6, 8, 9, 10
Probability = 7/10
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8) Probability of selecting a 3 or smaller
Numbers ≤ 3: 1, 2, 3 →
3 numbers
Probability = 3/10
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9) Probability of selecting an 8 or greater
Numbers ≥ 8: 8, 9, 10 →
3 numbers
Probability = 3/10
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10) Probability of selecting factors of 4 AND factors of 6
First, list factors of 4:
→ 1, 2, 4
Factors of 6:
→ 1, 2, 3, 6
Now, which numbers are factors of BOTH 4 and 6?
→ Common factors: 1, 2 →
2 numbers
Probability = 2/10 =
1/5
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Final Answer:
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
Parent Tip: Review the logic above to help your child master the concept of probability worksheet 5th grade.
