Objective B: Multiplication Rule for Independent Events If and are independent events, then Example 1: If 36% of college students are underweight, find the probability that if three college students are selected at random, all will be underweight. Independent case (1st underweight and 2nd underweight and 3rd underweight) P (1st underweight) * (2nd underweight) * (3rd underweight) P P P = 0.36*0.36*0.36 0.047 ≈ Example 2: If 25% of U.S. federal prison inmates are not U.S. citizens, find the probability that two randomly selected federal prison inmates will be U.S. citizens. (1st U. S. citizen and 2nd U. S. citizen) P = (1st U. S. citizen) * (2nd U. S. citizen) P P = 0.75 * 0.75 0.563 ≈ Objective C: At-Least Probabilities Probabilities involving the the Complement Rule. The phrase at phrase “at least” typically use than or For example, a person must be at least 17 years old to least means “greater equal to.” see an R-rated movie. Example 1: If you make random guesses for four multiple-choice test questions (each with five possible answers), what is the probability of getting at least one correct? Direct method: (at least one correct) P = (one correct) + (two correct) + (three correct) + (four correct) P P P P Indirect method: What is the opposite of at least one correct? None correct. (none correct) = * * * = P (at least one correct) = 1- (none correct) P P = 1- 0.590 ≈
Objective B: Multiplication Rule for Independent Events If and are independent events, then Example 1: If 36% of college students are underweight, find the probability that if three college students are selected at random, all will be underweight. Independent case P (1st underweight and 2nd underweight and 3rd underweight) P (1st underweight) * P (2nd underweight) * P (3rd underweight) = 0.36*0.36*0.36 ≈ 0.047 Example 2: If 25% of U.S. federal prison inmates are not U.S. citizens, find the probability that two randomly selected federal prison inmates will be U.S. citizens. P (1st U. S. citizen and 2nd U. S. citizen) = P (1st U. S. citizen) * P (2nd U. S. citizen) = 0.75 * 0.75 ≈ 0.563 Objective C: At-Least Probabilities Probabilities involving the phrase “at least” typically use the Complement Rule. The phrase at least means “greater than or equal to.” For example, a person must be at least 17 years old to see an R-rated movie. Example 1: If you make random guesses for four multiple-choice test questions (each with five possible answers), what is the probability of getting at least one correct? Direct method: P (at least one correct) = P (one correct) + P (two correct) + P (three correct) + P (four correct) Indirect method: What is the opposite of at least one correct? None correct. P (none correct) = * * * = P (at least one correct) = 1- P (none correct) = 1- ≈ 0.590