Compound Events Worksheet | Fun and Engaging 7th Grade PDF Worksheets - Free Printable

I'll solve this step by step, working through each section carefully.

## Section A: Probability of an event not happening

The key concept here is that if P(A) is the probability of an event happening, then P'(A) = 1 - P(A) is the probability of it NOT happening.

1) P(A) = 3/4
P'(A) = 1 - 3/4 = 4/4 - 3/4 = 1/4

2) P(B) = 0.69
P'(B) = 1 - 0.69 = 0.31

3) P(C) = 2/7
P'(C) = 1 - 2/7 = 7/7 - 2/7 = 5/7

4) P(D) = 57%
First convert to decimal: 57% = 0.57
P'(D) = 1 - 0.57 = 0.43 = 43%

5) P(E) = 0.125
P'(E) = 1 - 0.125 = 0.875

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## Section B: Mutually Exclusive Events

Events are mutually exclusive if they CANNOT happen at the same time (they have no outcomes in common).

The spinner has numbers: 1, 2, 3, 4, 5, 6, 7, 8

1) Landing on 2 and 8
- Event 1: {2}
- Event 2: {8}
- These cannot both happen on one spin
- YES, mutually exclusive ✓

2) Landing on a number less than 4 and greater than 4
- Event 1 (less than 4): {1, 2, 3}
- Event 2 (greater than 4): {5, 6, 7, 8}
- No overlap between these sets
- YES, mutually exclusive ✓

3) Landing on a factor of 8 and an odd number
- Factors of 8: {1, 2, 4, 8}
- Odd numbers: {1, 3, 5, 7}
- They share the number 1!
- NO, not mutually exclusive ✗

4) Landing on 5 and a prime number
- Event 1: {5}
- Prime numbers on spinner: {2, 3, 5, 7}
- 5 is in both sets!
- NO, not mutually exclusive ✗

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## Section C: Exhaustive Events

Events are exhaustive if together they cover ALL possible outcomes (every number 1-8 must be included).

1) Landing on 2 and 8
- Outcomes covered: {2, 8}
- Missing: {1, 3, 4, 5, 6, 7}
- NO, not exhaustive

2) Landing on a number less than 4 and greater than 4
- Less than 4: {1, 2, 3}
- Greater than 4: {5, 6, 7, 8}
- Combined: {1, 2, 3, 5, 6, 7, 8}
- Missing: {4}
- NO, not exhaustive ✗

3) Landing on a factor of 8 or an odd number
- Factors of 8: {1, 2, 4, 8}
- Odd numbers: {1, 3, 5, 7}
- Combined (using "or"): {1, 2, 3, 4, 5, 7, 8}
- Missing: {6}
- NO, not exhaustive ✗

4) Landing on 5 and a prime number
- This says "and" not "or", so we need outcomes that are BOTH 5 AND prime
- Since 5 is prime, this is just {5}
- Clearly doesn't cover all outcomes
- NO, not exhaustive ✗

Example of exhaustive events:
One simple example: "Landing on an even number OR landing on an odd number"
- Even: {2, 4, 6, 8}
- Odd: {1, 3, 5, 7}
- Together they cover all numbers 1-8 ✓

Another example: "Landing on a number ≤ 4 OR landing on a number > 4"
- ≤ 4: {1, 2, 3, 4}
- > 4: {5, 6, 7, 8}
- Together they cover all numbers 1-8 ✓

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Final Answer:

Section A:
1) P'(A) = 1/4
2) P'(B) = 0.31
3) P'(C) = 5/7
4) P'(D) = 43% (or 0.43)
5) P'(E) = 0.875

Section B:
1) YES (mutually exclusive)
2) YES (mutually exclusive)
3) NO (not mutually exclusive)
4) NO (not mutually exclusive)

Section C:
1) NO (not exhaustive)
2) NO (not exhaustive)
3) NO (not exhaustive)
4) NO (not exhaustive)

Example of exhaustive events: Landing on an even number OR landing on an odd number