Activity 7
MATH 216: Statistical Thinking
Probability Rules and Applications
Time Allocation: 15 minutes total
Part 1: Multiplicative Rule Practice (5 minutes)
Scenario: Two balls selected without replacement from box with r red and b blue balls.
Calculate:
\(P(\text{First red AND second blue})\) = _________________________
\(P(\text{Second ball blue})\) = _________________________________
Show formulas and work:
Part 2: Law of Total Probability (5 minutes)
Given:
- \(P(B) = 0.6\), \(P(B^\complement) = 0.4\)
- \(P(A \mid B) = 0.7\), \(P(A \mid B^\complement) = 0.3\)
Calculate: \(P(A)\) = ____________________________________
Show work using law of total probability:
Part 3: Independence and Multiplication (5 minutes)
Die Roll Events:
- A = {Even number}
- B = {Number ≤ 4}
Check Independence:
- \(P(A)\) = ______, \(P(B)\) = ______, \(P(A \cap B)\) = ______
- Does \(P(A \cap B) = P(A) \times P(B)\)? □ Yes □ No
- Therefore, A and B are: □ Independent □ Dependent
Real-world Application:
- 25% of divorced couples are “fiery foes”
- \(P(\text{both couples fiery foes in sample of 2})\) = _______________
- \(P(\text{all 10 couples fiery foes in sample of 10})\) = _____________