Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Advanced Mathematical Concepts Chapter 13 Lesson 13-3 Example 1 ENTERTAINMENT Each year, about 50,000 people audition to become contestants on a show that seeks to find the best singer and award him or her a recording contract. Only 12 are chosen to be finalists on the show. What is the probability of being selected as a finalist? Use the probability formula. Since 12 people are selected as finalists, s = 12. The denominator, s + f, represents the total number of people auditioning, those selected as finalists, s, and those not selected, f. So, s + f = 50,000. P(12) = 3 12 or 12,500 50,000 s P(s) = s + f The probability of any one person being selected as a finalist is 3 or 0.024%. 12,500 Example 2 A cookie jar contains 9 chocolate chip, 5 oatmeal, and 6 sugar cookies. a. What is the probability that a cookie selected at random will be a sugar cookie? b. What is the probability that a cookie selected at random will not be chocolate chip? a. The probability of selecting a sugar cookie is P(sugar). There are 6 ways to select a sugar cookie from the jar, and 9 + 5 or 14 ways not to select a sugar cookie. So, s = 6 and f = 14. 6 3 P(sugar) = 6 + 14 or 10 s P(s) = s + f 3 The probability of selecting a sugar cookie is 10. b. There are 9 ways to choose a chocolate chip cookie. So there are 11 ways not to select a chocolate chip cookie. 11 11 P(not chocolate chip) = 9 + 11 or 20 11 The probability of not selecting a chocolate chip cookie is 20. Advanced Mathematical Concepts Chapter 13 Example 3 A class of 15 children is made up 6 girls and 9 boys. If all their names are placed in a hat and then 4 names are selected from the hat at random, what is the probability that the names chosen will be girls? There are C(6, 4) ways to choose 4 out of 6 girls, and C(15, 4) ways to select 4 out of 15 children. C(6, 4) P(4 girls) = C(15, 4) 6! 2! 4! 1 = 15! or 91 11! 4! The probability of selecting four girls is 1 . 91 Example 4 An automobile manufacturer determines that for every 20 cars it produces of a particular model, 2 will have a defective oil tank. If a car dealership has 20 cars of this model on its lot and it sells 4 of them in one week, what is the probability that at least 1 one of the cars sold has a defective oil tank? The complement of selecting at least 1 car with a defective oil tank is selecting no cars with defective oil tanks. That is, P(at least 1 defective oil tank) = 1 - P(no defective oil tank). P(at least 1 defective oil tank) = 1 - P(no defective oil tank) C(18, 4) =1C(20, 4) 3060 = 1 - 4845 0.3684210526 The probability of selling at least 1 car with a defective oil tank is about 37%. Advanced Mathematical Concepts Chapter 13 Example 5 A game at a town fair has children use a fishing rod with a magnet at the end of the fishing line to catch plastic fish floating in a tank of water. Underneath each fish is either the letter S or L. If a child catches a fish with the letter S, she may choose a small prize. If a child catches a fish with the letter L, he may choose a large prize. There are 40 fish with the letter S and 10 fish with the letter L. a. What is the probability that a child will catch a fish with the letter L? b. What are the odds that a child will win a large prize? 10 1 a. The probability that a child will catch a fish with the letter L is 50 or 5. b. To find the odds that a child will win a large prize, you to need to know the probability of a successful outcome and of a failing outcome. Let s represent catching a fish with the letter L and f represent not catching a fish with the letter L. P(s) = 1 5 P(f) = 4 5 Now find the odds. 1 P(s) 5 1 P(f) = 4 or 4 5 1 1 The odds that a child will win a large prize is 4. The ratio 4 is read “1 to 4.” Advanced Mathematical Concepts Chapter 13 Example 6 As a fundraiser, a school is holding a raffle. Out of the general pool of participants, 25 are selected to enter the grand prize drawing. Four grand prizes are to be given to 4 different individuals. If there are 15 men and 10 women selected for the grand prize drawing, and names are drawn at random, what are the odds that 1 will be male and 3 will be female? First, determine the total number of possible groups. C(15, 1) C(10, 3) number of groups of 1 male number of groups of 3 females Using the Basic Counting Principle we can find the number of possible groups of 1 male and 3 females. C(15, 1) C(10, 3) = 15! 10! or 1800 possible groups 14! 1! 7! 3! The total number of groups of 4 recipients out of the 25 who qualified is C(25, 4) or 12,650. So, the number of groups that do not have 1 male and 3 females is 12,650 - 1800 or 10,850. Finally, determine the odds. P(s) = 1800 12,650 P(f) = 10,850 12,650 1800 36 12,650 odds = or 217 10,850 12,650 36 1 Thus, the odds of selecting a group of 3 females and 1 male are 217 or close to 6.