Cogito
Probability and Statistics · Chapter 4 · Lesson 1
And, Or, and Independence
Combining two events.
12 problems · about 22 minutes · TEKS P.S.2.D, S-CP.A.2
What this lesson teaches
The student applies the addition and multiplication rules and tests events for independence.
- For independent events, multiply to get "and".
- For "or", add and subtract the overlap.
- Mutually exclusive is not the same as independent.
Warm Up
Straightforward practice. Get the method working first.
5 problemsP(A) = 0.5, P(B) = 0.2, independent. What is P(A and B)?
Answer 0.1
Why 0.1.
Why does the addition rule subtract P(A and B)?
Answer The overlap would otherwise be counted twice.
Why It removes the double count.
P(A) = 0.3, P(B) = 0.5, independent. P(A and B)?
Answer 0.15
Why Multiply.
P(A) = 0.2, P(B) = 0.3, mutually exclusive. P(A or B)?
Answer 0.5
Why No overlap to subtract.
Two dice. Probability both show six, as a decimal to three places?
Answer 0.028
Why 1/36.
Build It Up
The same ideas with more to keep track of.
3 problemsP(A) = 0.6, P(B) = 0.5, P(A and B) = 0.3. P(A or B)?
Answer 0.8
Why 0.6 + 0.5 − 0.3.
Are mutually exclusive events independent? 1 for yes, 0 for no.
Answer 0
Why One occurring makes the other impossible.
Three fair coins. Probability all heads, as a decimal to three places?
Answer 0.125
Why 0.5 cubed.
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 an ace and drawing a king on one card
Why Ask whether the first result changes the second chance.
P(A) = 0.4, P(B) = 0.25, independent. P(A and B)?
Answer 0.1
Why Multiply.
The Two Coins: Two fair coins. Probability both are heads, as a decimal?
Answer 0.25
Why 0.25.
The Overlap: P(A) = 0.5, P(B) = 0.4, P(A and B) = 0.2. What is P(A or B)?
Answer 0.7
Why 0.7.