Probability worksheet for students to calculate the likelihood of selecting specific types of numbers from 1 to 10.

Sure! Let’s solve each of the 10 probability problems step by step. Since a number is chosen at random from 1 to 10, we assume each number has an equal chance of being selected. So, the total number of possible 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 → 5 numbers

Probability = favorable outcomes / total outcomes = 5/10 = 1/2

✔ Answer: 1/2

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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

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3) Probability of selecting an odd number

Odd numbers from 1 to 10:
→ 1, 3, 5, 7, 9 → 5 numbers

Probability = 5/10 = 1/2

✔ Answer: 1/2

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4) Probability of NOT selecting a multiple of 2

This is the complement of problem #1.

We know P(multiple of 2) = 5/10 = 1/2
So, P(not multiple of 2) = 1 - 1/2 = 1/2

Alternatively, non-multiples of 2 are the odd numbers: 1,3,5,7,9 → 5 numbers → 5/10 = 1/2

✔ Answer: 1/2

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5) Probability of NOT selecting a multiple of 3

Complement of problem #2.

P(multiple of 3) = 3/10
So, P(not multiple of 3) = 1 - 3/10 = 7/10

Alternatively, numbers not multiples of 3: 1,2,4,5,7,8,10 → 7 numbers → 7/10

✔ Answer: 7/10

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6) Probability of NOT selecting a multiple of 2 OR a multiple of 3

This means: not (multiple of 2 or multiple of 3)
→ This is the same as selecting a number that is neither a multiple of 2 nor a multiple of 3.

First, find numbers that are multiples of 2 or 3:

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 neither: 1,5,7 → 3 numbers

Probability = 3/10

✔ Answer: 3/10

*(Note: You could also use inclusion-exclusion:
P(A or B) = P(A) + P(B) - P(A and B)
= 5/10 + 3/10 - 1/10 (since 6 is common) = 7/10
Then P(neither) = 1 - 7/10 = 3/10)*

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7) Probability of selecting a multiple of 2 OR a multiple of 3

From above, we found that there are 7 numbers that are multiples of 2 or 3: 2,3,4,6,8,9,10

So, probability = 7/10

✔ Answer: 7/10

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8) Probability of selecting a 3 or smaller

Numbers ≤ 3: 1, 2, 3 → 3 numbers

Probability = 3/10

✔ Answer: 3/10

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9) Probability of selecting an 8 or greater

Numbers ≥ 8: 8, 9, 10 → 3 numbers

Probability = 3/10

✔ Answer: 3/10

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10) Probability of selecting factors of 4 AND factors of 6

This means: numbers that are common factors of both 4 and 6 — i.e., factors of GCD(4,6).

Factors of 4: 1, 2, 4
Factors of 6: 1, 2, 3, 6
Common factors: 1, 2 → 2 numbers

So, probability = 2/10 = 1/5

✔ Answer: 1/5

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## ✔ Final Answers Summary:

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 this in worksheet format or with diagrams!