advanced math topics

Advanced Math Topics

Chapter 5 Review Olympics

• One sheet per player

• Make an answer column on the left hand side of your sheet

• Work together to solve each question

• Winning team earns a reward

• We will go over the process and answers for each

BRONZE

1 point

1) You select three cards from a deck ofcards with replacement. Find the probabilitythat you selected a red card first, a heartsecond, and an ace third. Write your answer as a reduced fraction.

2) You select two cards from a deckwithout replacement. Find the probabilityyou selected an 8 of spades, then a club.Write your answer as a percent rounded to the nearest hundredth of a percent.

3) You select a student at random. Find theprobability that you selected a student whose favorite soda is Root Beer. Leaveas a reduced fraction.

Coke Pepsi Mt. Dew Root Beer-------------------------------------------------------------------------------------------------Juniors 243 198 107 88-------------------------------------------------------------------------------------------------Seniors 222 201 99 104

Favorite Sodas at SRVHS

4) You select a student at random. Find theprobability that you selected a studentwhose favorite soda is Coke given that thestudent is a senior. Leave as a reduced fraction.



5) You select a student at random. Find theprobability that you selected a studentwhose favorite soda is Pepsi and a studentwho is a junior. Leave as a reduced fraction.



SILVER

2 points

6) You select a card from a standard deck.Find the probability that it is a heart or a redcard. Leave as a reduced fraction.

7) You select a card from a standard deck.Find the probability that it is a heart or a jack.Leave as a reduced fraction.

8) The probability that you take the test is90/100. The probability that you earn an Ais 2/3. What is the probability that you takethe test and do not get an A? Leave your answer as a reducedfraction.

9) The probability that a college studentstudies before a test is 0.87. The probability that a student studies before atest and is on the Dean’s List is 0.77. Find the probability thata randomly selected student who studies before a test is alsoon the Dean’s List. Write your answer as a percent roundedto the nearest hundredth of a percent.

GOLD

3 points

10) There are 500 strawberry drinks, 300orange drinks, and 200 berry drinks ona supermarket shelf. The probability thatEach drink has contains a harmful bacteria is 0.02, 0.03, and 0.01, respectively. If a drink is randomly selected from the shelfand it contains the harmful bacteria, find the probability thatit is a berry drink. Write your answer as a percent roundedto the nearest hundredth of a percent.

11) The probability of getting on the Wallof Fame is 0.04. You randomly select3 people from the class, find the probabilitythat at least one person made the Wall of Fame.Hint: Think complement. Write your answer as a percent roundedto the nearest hundredth of a percent.

• Rows 1 and 2 Trade Papers



• Score only one sheet, then add it to their teammate’s score.

• Points: Gold = 3 Silver = 2 Bronze = 1

• If there is more than 1 part, all parts must be correct to get the points

BRONZE

1 point

1) You select three cards from a deck ofcards with replacement. Find the probabilitythat you selected a red card first, a heartsecond, and an ace third. Write your answer as reduced fraction.

Answer: 1/104

Process: ½ x ¼ x 1/13

Answer: .49%

Process: p(8 of spades) x p(club | 8 of spades) = 1/52 x 13/51

2) You select two cards from a deckwithout replacement. Find the probabilityyou selected an 8 of spades, then a club.Write your answer as a percent rounded to the nearest hundredth of a percent.

Answer: 96/631

Process: (88 + 104)/total # of students

192/ 1262

3) You select a student at random. Find theprobability that you selected a student whose favorite soda is Root Beer. Leaveas a reduced fraction.



Answer: 111/313

Process: P(Coke | senior) = P(coke and senior)/P(senior) = 222/626

4) You select a student at random. Find theprobability that you selected a studentwhose favorite soda is Coke given that thestudent is a senior. Leave as a reduced fraction.


Answer: 99/631

Process: (Junior and Pepsi)/total 198/1262

5) You select a student at random. Find theprobability that you selected a studentwhose favorite soda is Pepsi and a studentwho is a junior. Leave as a reduced fraction.


SILVER

2 points

Answer: ½

Process: p(heart) + p(red card) – p(both red card and heart) ¼ + ½ - ¼

6) You select a card from a standard deck.Find the probability that it is a heart or a redcard. Leave as a reduced fraction.

Answer: 4/13

Process: p(heart) + p(jack) – p(jack of hearts) 13/52 + 4/52 – 1/52

7) You select a card from a standard deck.Find the probability that it is a heart or a jack.Leave as a reduced fraction.

Answer: 3/10

Process: p(not an A) = 1 – p(A) = 1 – 2/3 = 1/3

p(take it) x p(not an A | take the test) 90/100 x 1/3 = 9/10 x 1/3

8) The probability that you take the test is90/100. The probability that you earn an Ais 2/3. What is the probability that you takethe test and do not get an A? Leave your answer as a reducedfraction.

GOLD

3 points

Answer: 88.51%

Process: p(Dean’s List | studies before a test) = p(both) / p(studies before a test) = 0.77 / 0.87 =

9) The probability that a college studentstudies before a test is 0.87. The probability that a student studies before atest and is on the Dean’s List is 0.77. Find the probability thata randomly selected student who studies before a test is alsoon the Dean’s List. Write your answer as a percent roundedto the nearest hundredth of a percent.

Answer: 9.52%

Process: Bayes’ Formula [(200/1000) x (0.01)] / [(200/1000) x 0.01 + (500/1000) x 0.02 + (300/1000) x 0.03]

10) There are 500 strawberry drinks, 300orange drinks, and 200 berry drinks ona supermarket shelf. The probability thatEach drink has contains a harmful bacteria is 0.02, 0.03, and 0.01, respectively. If a drink is randomly selected from the shelfand it contains the harmful bacteria, find the probability thatit is a berry drink. Write your answer as a percent roundedto the nearest hundredth of a percent.

Answer: 11.53%

Process: The complement of at least one person made it is no one made it. Thus p(at least one made it) = 1 – p(no one made it) = 1 – p(no) x p(no) x p(no) = 1 – 0.96 x 0.96 x 0.96

11) The probability of getting on the Wallof Fame is 0.04. You randomly select3 people from the class, find the probabilitythat at least one person made the Wall of Fame.Hint: Think complement. Write your answer as a percent roundedto the nearest hundredth of a percent.

Answer: 11.06%

Tiebreaker) The probability of getting on the Wallof Fame is 0.04. You randomly select3 people from the class, find the probabilityexactly one person made the Wall of Fame.Sa your answer as a percent roundedto the nearest hundredth of a percent.

HW

• P. 280 #1-10

• To study, look at this slideshow, past slideshows, the book, the chapter review, etc.

• Winners: Do the Odds

• Test Tomorrow

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