Worksheet on probability rules including mutually exclusive events and calculating probabilities for various scenarios.

Absolutely! Let’s solve each problem step by step, explaining the reasoning behind each answer.

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## I. Determine whether these events are mutually exclusive.

Mutually exclusive events cannot happen at the same time — if one occurs, the other cannot. In probability terms:
> P(A and B) = 0

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1) Roll a die: get an even number and get a number less than 3

- Even numbers on a die: {2, 4, 6}
- Numbers less than 3: {1, 2}
- Intersection: {2} → They can both happen (rolling a 2)

✔ Not mutually exclusive

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2) Roll a die: get a prime number and get an odd number

- Prime numbers on a die: {2, 3, 5}
- Odd numbers: {1, 3, 5}
- Intersection: {3, 5} → They can both happen

✔ Not mutually exclusive

*(Note: 2 is prime but even — so not all primes are odd, but some overlap exists.)*

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3) Roll a die: get a number greater than 3 and get a number less than 3

- Greater than 3: {4, 5, 6}
- Less than 3: {1, 2}
- Intersection: {} → No overlap

✔ Mutually exclusive

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4) Select a student in the classroom: student has blond hair and blue eyes

- A student can have both blond hair AND blue eyes — these are independent traits.
- Example: Many people have both.

✔ Not mutually exclusive

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5) Select a student at UGA: student is a sophomore and the student is a business major

- A student can be both a sophomore AND a business major — no conflict.

✔ Not mutually exclusive

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6) Select any high school course: the course is calculus and the course is English

- A single course cannot be both calculus AND English — they are different subjects.

✔ Mutually exclusive

*(Unless it's a combined course like “Math & Literature,” which is unlikely in standard high schools.)*

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## II. Find the following probabilities

We use the basic probability formula:
> P(event) = (Number of favorable outcomes) / (Total possible outcomes)

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7) Automobile dealer selects a month for annual sale. Probability it’s September or October.

- Total months: 12
- Favorable: September, October → 2 months

P = 2/12 = 1/6

✔ Answer: 1/6

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8) Community swimming pool: 2 managers, 8 lifeguards, 3 concession clerks, 2 maintenance people. Random person selected — probability they’re a lifeguard OR manager.

- Total people = 2 + 8 + 3 + 2 = 15
- Lifeguards + Managers = 8 + 2 = 10

P = 10/15 = 2/3

✔ Answer: 2/3

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9) Convention: 7 math, 5 computer science, 3 statistics, 4 science instructors. Random instructor selected — probability they’re math OR science instructor.

- Total instructors = 7 + 5 + 3 + 4 = 19
- Math OR Science = 7 + 4 = 11

*(Note: “Science” here likely refers to the separate category of “science instructors” — not including computer science or statistics unless specified. The problem says “math or science”, so we assume only those two categories.)*

P = 11/19

✔ Answer: 11/19

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10) Blockbuster movie rentals: 170 horror, 230 drama, 310 romance, 150 comedies. Random movie rented — probability it’s romance OR comedy.

- Total movies = 170 + 230 + 310 + 150 = 860
- Romance + Comedy = 310 + 150 = 460

P = 460 / 860

Simplify: divide numerator and denominator by 20 → 23/43

✔ Answer: 23/43

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## ✔ Final Answers Summary:

I. Mutually Exclusive?

1. ✘ No
2. ✘ No
3. ✔ Yes
4. ✘ No
5. ✘ No
6. ✔ Yes

II. Probabilities:

7. 1/6
8. 2/3
9. 11/19
10. 23/43

Let me know if you’d like visual diagrams or further explanations!