Cogito
Integrated Math 2 · Chapter 8 · Lesson 1
Probability of Compound Events
Combining two events.
12 problems · about 21 minutes · S-CP.A.1, S-CP.B.7
What this lesson teaches
The student computes probabilities of compound events using the addition and multiplication rules.
- Multiply for "and" when events are independent.
- Add for "or", subtracting the overlap.
- The complement rule handles "at least one" fastest.
Warm Up
Straightforward practice. Get the method working first.
5 problemsP(A) = 0.5, P(B) = 0.3, independent. What is P(A and B)?
Answer 0.15
Why 0.15.
Why does the or rule subtract the overlap?
Answer It would otherwise be counted in both terms.
Why It removes the double count.
P(A) = 0.4, P(B) = 0.5, independent. P(A and B)?
Answer 0.2
Why Multiply.
P(A) = 0.3, P(B) = 0.2, mutually exclusive. P(A or B)?
Answer 0.5
Why No overlap.
P(A) = 0.6. What is P(not A)?
Answer 0.4
Why 1 − 0.6.
Build It Up
The same ideas with more to keep track of.
3 problemsP(A) = 0.5, P(B) = 0.4, P(A and B) = 0.2. P(A or B)?
Answer 0.7
Why 0.5 + 0.4 − 0.2.
Two dice. Probability both show six, to three decimal places?
Answer 0.028
Why 1 ÷ 36.
A bag has 4 red and 6 blue. Probability of red, as a decimal?
Answer 0.4
Why 4 ÷ 10.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each pair by whether the events are independent.
Answer Independent: Two separate coin tosses, Rolling a die twice · Not independent: Two draws from a bag without replacement, Drawing a red card and drawing a spade on one card
Why Ask whether the first result changes the second chance.
P(A) = 0.25, P(B) = 0.8, independent. P(A and B)?
Answer 0.2
Why Multiply.
The Two Coins: Two fair coins. Probability both are heads, as a decimal?
Answer 0.25
Why 0.25.
The Complement: Three fair coins. Probability of at least one head, as a decimal?
Answer 0.875
Why 0.875.