Probability Addition & Multiplication Rules

Name:

Date:

📊 Part 1: Identifying Rules and Events

1. Which rule would you use to find P(A or B) when events A and B are mutually exclusive?

Addition rule: P(A or B) = P(A) + P(B)

Multiplication rule: P(A and B) = P(A) × P(B)

Addition rule: P(A or B) = P(A) + P(B) - P(A and B)

2. A bag contains 5 red balls and 3 blue balls. You draw one ball, replace it, then draw another. The events "first ball is red" and "second ball is blue" are:

Independent

Dependent

Mutually exclusive

3. Which of the following pairs of events are mutually exclusive? (Check all that apply)

Rolling a 3 or rolling an even number on a die

Drawing a heart or drawing a red card from a deck

Being born in January or being born in March

Raining today or being sunny today

🧮 Part 2: Applying the Rules

4. At Auckland Grammar, 60% of students play rugby and 40% play cricket. If 25% play both sports, what is the probability a randomly selected student plays rugby OR cricket?

Answer: ___________

5. A card is drawn from a standard deck, then a second card is drawn WITHOUT replacement. Find P(both cards are aces).

Answer: ___________

6. In Christchurch, the probability of rain on any given day is 0.3. Assuming independence, what is the probability it rains on both Monday AND Tuesday?

Answer: ___________

7. A box contains 8 chocolate biscuits and 12 plain biscuits. If you select 2 biscuits without replacement, find P(first is chocolate OR second is chocolate). Show your working clearly.

Answer: ___________

💭 Part 3: Critical Thinking

8. A news article claims: "Since 30% of accidents happen on weekends and 25% happen in wet conditions, there's a 55% chance an accident happens on a weekend OR in wet conditions."

a) Explain what assumption the article is making about these events:

b) Is this assumption reasonable? Why or why not?

c) What additional information would you need to calculate the correct probability?

9. Explain in your own words when you would use the addition rule versus the multiplication rule in probability problems.