Activity 6

MATH 216: Statistical Thinking

Conditional Probability and Ethical Analysis

Time Allocation: 15 minutes total

Part 1: Basic Probability Concepts (5 minutes)

Question: If \(P(A) = 0.3\), what is \(P(A^\complement)\)?

□ 0.3
□ 0.7
□ 0.5
□ 0.1

Explanation: _________________________________________________________

Additional Practice:

If \(P(B) = 0.6\), then \(P(B^\complement)\) = ______________________
If \(P(C) = 0.25\), then \(P(C^\complement)\) = _____________________
Complementary probability rule: ___________________

Part 2: Conditional Probability Calculation (5 minutes)

Business Ethics Study:

55% of executives cheated at golf
20% cheated at golf AND lied in business

Calculate: \(P(\text{Lied in business} \mid \text{Cheated at golf})\) = ____________________

Show your work:

Interpretation: This means that ______% of executives who cheated at golf also lied in business.

Part 3: Smoking and Cancer Analysis (5 minutes)

Medical Research Scenario:

Sample point probabilities for smoking and cancer:

\(P(\text{Smoker} \cap \text{Cancer}) = 0.05\)
\(P(\text{Smoker} \cap \text{No Cancer}) = 0.20\)
\(P(\text{Non-smoker} \cap \text{Cancer}) = 0.03\)
\(P(\text{Non-smoker} \cap \text{No Cancer}) = 0.72\)

Individual probabilities (calculate these first):

$P() = $ ___________________________
$P() = $ _______________________
$P() = $ ___________________________
$P() = $ _________________________

Calculate Conditional Probabilities:

\(P(\text{Cancer} \mid \text{Smoker})\) = ___________________________
\(P(\text{No Cancer} \mid \text{Smoker})\) = ________________________
\(P(\text{Cancer} \mid \text{Non-smoker})\) = _______________________

Interpretation: The risk of cancer is ______ times higher for smokers compared to non-smokers.