Activity 5

MATH 216: Statistical Thinking

Probability Concepts Practice

Time Allocation: 15 minutes total

Part 1: Sample Space Construction (5 minutes)

Scenario: Rolling a die and tossing a coin simultaneously.

Instructions:

  1. List the complete sample space for this experiment
  2. Calculate the total number of possible outcomes
  3. Identify specific probabilities

Complete Sample Space:

Calculations:

  • Total number of outcomes: _________________________
  • \(P(\text{rolling 2 AND heads})\): __________________________
  • \(P(\text{rolling even number AND tails})\): _________________

Part 2: Probability Calculations (5 minutes)

Multiple Choice: What is the probability of rolling a 2 on a fair six-sided die?

  • □ 1/6
  • □ 1/3
  • □ 1/2
  • □ 1/1

Explanation: _________________________________________________________

Additional Calculations:

  • \(P(\text{rolling number} > 4)\): ___________________________
  • \(P(\text{rolling prime number})\): _________________________
  • \(P(\text{rolling number divisible by 3})\): _________________

Part 3: Empirical vs Theoretical Probability (5 minutes)

Simulated Data: 200 die rolls

Die Roll Distribution:
1 : 33 rolls ( 16.5 %)
2 : 31 rolls ( 15.5 %)
3 : 32 rolls ( 16 %)
4 : 28 rolls ( 14 %)
5 : 34 rolls ( 17 %)
6 : 42 rolls ( 21 %)

Even numbers: 101 ( 50.5 %)

Analysis:

  • Empirical \(P(\text{even})\): _______________________________
  • Theoretical \(P(\text{even})\): _____________________________
  • Difference: _____________________________________
  • Reason for difference: ___________________________