University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

342

Pages:

3
Author:

3dy0s3lincd53

Class Review Content: Disjoint Events Exercises 1 and 2: Problem 1: P(A) = 0.4, P(B) = 0.2 P(A or B) = P(A) + P(B) = 0.4 + 0.2 = 0.6 Problem 2: P(A) = 1/3, P(B) = 1/2 P(A or B) = P(A) + P(B) = 1/3 + 1/2 = 5/6 Problem 3: At the high school swim meet, you estimate a 40% chance you will win and a 35% chance your friend will win the 50 Freestyle event. P(You or Friend) = P(You) + P(Friend) = 0.4 + 0.35 = 0.75 Joint Events Exercises 4 and 5: (You roll a die) Problem 4: Event A: Roll an even number Event B: Roll an odd number P(A or B) = P(A) + P(B) = 3/6 + 3/6 = 6/6 = 1 (This is a certainty) Problem 5: Event A: Roll an even number Event B: Roll a number greater than 3 P(A or B) = P(A) + P(B) - P(A and B) = 3/6 + 3/6 - 2/6 = 4/6 = 2/3 Problem 6: Your cat has a 75% probability of having a kidney disorder or is diabetic, with a 40% chance of having a kidney disorder and a 50% chance of being diabetic. P(Kidney) + P(Diabetic) - P(Kidney and Diabetic) = P(Kidney or Diabetic) 0.4 + 0.5 - P(Kidney and Diabetic) = 0.75 P(Kidney and Diabetic) = 0.15 Problem 7: A game show has three doors: Grand Prize, Nice Prize, and Dummy Prize. A table shows the probabilities of winning each prize for each door. Part a: Find the probability of winning the Grand Prize or Nice Prize if you choose Door 1. P(Grand Prize or Nice Prize) = 0.25 + 0.4 = 0.65 Part b: Find the probability of winning the Grand Prize or Nice Prize if you choose Door 2. P(Grand Prize or Nice Prize) = 0.45 + 0.25 = 0.7 Class Review Instructions: Find the number of ways that you can arrange (a) all of the letters and (b) 2 of the letters in the given word. HAT PORT CHURN In Exercises 4-9, evaluate the expression. 4. 4P3 5. 6P2 6. 8P1 7. 5P4 8. 9P5 9. 11P0 Fifteen sailboats are racing in a regatta. In how many different ways can three sailboats finish first, second, and third? 11. 1 Your bowling team and your friend's bowling team are in a league with 6 other teams. In tonight's competition, find the probability that your friend's team finishes first and your team finishes second. 2 Solutions: Problem 1: a) 3! = 6 b) 3P2 = 3!/(3-2)! = 3! = 6 Problem 2: a) 4! = 24 b) 4P2 = 4!/(4-2)! = 4! / 2! = 12 Problem 3: a) 5! = 120 b) 5P2 = 5!/(5-2)! = 5! / 3! = 20 Problem 4: 4P3 = 4!/(4-3)! = 4! = 24 Problem 5: 6P2 = 6!/(6-2)! = 6! / 4! = 30 Problem 6: 8P1 = 8!/(8-1)! = 8! / 7! = 8 Problem 7: 5P4 = 5!/(5-4)! = 5! = 120 Problem 8: 9P5 = 9!/(9-5)! = 9! / 4! = 15,120 Problem 9: 11P0 = 11!/(11-0)! = 11! / 11! = 1 Problem 10: 15P3 = 15!/(15-3)! = 15! / 12! = 2,730 ways Problem 11: Number of ways for top 2 finishes: 8P2 = 8!/(8-2)! = 8! / 6! = 56 Probability: 1/56 = 0.0179 (or 1.79%)