Tasks 07-02 - Basic Probability

Section 07: Probability & Statistics

Problem 1: Sample Spaces (x)

Define the sample space for each experiment:

  1. Rolling a six-sided die
  2. Flipping two coins
  3. Drawing a card from a standard deck and noting its suit
  4. A customer rating satisfaction on a scale of 1-5

Problem 2: Basic Probability Calculations (x)

A fair six-sided die is rolled. Find:

  1. \(P(\text{rolling a 4})\)
  2. \(P(\text{rolling an even number})\)
  3. \(P(\text{rolling greater than 4})\)
  4. \(P(\text{rolling a 7})\)
  5. \(P(\text{not rolling a 6})\)

Problem 3: Addition Rule (x)

In a class of 100 students: - 45 study German - 35 study French - 15 study both German and French

  1. Find \(P(\text{German})\)
  2. Find \(P(\text{German or French})\)
  3. Find \(P(\text{neither German nor French})\)
  4. Find \(P(\text{German only})\)

Problem 4: Independence (xx)

Two machines operate independently. Machine A works 95% of the time, Machine B works 90% of the time.

  1. Find \(P(\text{both work})\)
  2. Find \(P(\text{neither works})\)
  3. Find \(P(\text{at least one works})\)
  4. Find \(P(\text{exactly one works})\)

Problem 5: Cards (xx)

A card is drawn from a standard 52-card deck. Find:

  1. \(P(\text{Ace})\)
  2. \(P(\text{Heart})\)
  3. \(P(\text{Ace or Heart})\)
  4. \(P(\text{Face card})\) (Jack, Queen, King)
  5. Are “Ace” and “Heart” mutually exclusive? Independent?

Problem 6: Business Application (xx)

A company surveyed 500 customers: - 320 are satisfied with the product - 280 are repeat customers - 200 are satisfied AND repeat customers

  1. Find \(P(\text{Satisfied})\)
  2. Find \(P(\text{Satisfied or Repeat})\)
  3. Find \(P(\text{Satisfied but not Repeat})\)
  4. Are satisfaction and repeat status independent?

Problem 7: Quality Control (xxx)

A factory produces items with a 3% defect rate. A sample of 5 items is randomly selected.

  1. Are these selections independent? Why or why not?
  2. Find \(P(\text{all 5 are good})\)
  3. Find \(P(\text{at least one is defective})\)
  4. Find \(P(\text{exactly one is defective})\)