Advanced Math Topics

Advanced Math Topics Chapter 4 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

There are 9 players on a baseball team. • if the pitcher bats last, how many different • batting orders are possible?

2) What is the sample space for… • Flipping 2 coins • Rolling 2 dice and flipping a coin • Flipping a coin 7 times

3) If the probability of the New York Mets winning a particular game is 3/7, what are the odds in favor of the Mets winning the game?

SILVER 2 points

4) A coin is tossed 6 times, find the probability of getting 2 tails. Leave your answer as a fraction.

5) How many 3-digit numbers larger than 600 can be formed from the digits 4, 5, 6, and 7 if repetition is not allowed?

6) How many ways can you arrange the letters of “combination.”

7) You are selecting a 4-person committee from the 50 Governors. There are 38 male Governors and 12 female Governors. How many different committees can be selected if you want to select 3 women and 1 man?

GOLD 3 points

8) Mr. and Mrs. Boyer have 4 children. What is the probability that their oldest and youngest child are girls? Hint: List out the sample space.

9) Two dice are rolled. If you roll a sum greater than 9, you win $4. Otherwise, you lose $1. What is your mathematical expectation? Round to the nearest penny.

10) Last year, the I.R.S. audited 2.3% of all tax returns. If a tax return is randomly selected, what are the odds in favor of it being audited?

11) Twelve cans of soda consisting of 4 Pepsi, 3 Coke, 2 Root Beer, and 3 Seven-up are placed on a shelf. In how many different ways can this be done if cans of the same brand stay together?

12) You are selecting a 4-person committee from the 50 Governors. There are 38 male Governors and 12 female Governors. Find the probability that the committee will consist of two males and two females. Put as a % rounded to the nearest hundredth.

Rows 1 and 2 Trade Papers • Rows 3 and 4 Trade Papers • Rows 5 and 6 Trade Papers • Score only one sheet, then add it to their teammate’s score. • Points: Gold = 3Silver = 2Bronze = 1 • If there is more than 1 part, all parts must be correct to get the points

BRONZE 1 point

There are 9 players on a baseball team. • if the pitcher bats last, how many different • batting orders are possible? Process: There are 8 spots to be filled. 8! Answer:40,320

2) What is the sample space for… • Flipping 2 coins • Rolling 2 dice and flipping a coin • Flipping a coin 7 times Process: Multiply the number of possibilities for each trial. a) 2 x 2 b) 6 x 6 x 2 c) 27 Answer: a) 4 b) 72 c) 128

3) If the probability of the New York Mets winning a particular game is 3/7, what are the odds in favor of the Mets winning the game? Process: 3 favorable outcomes to 4 unfavorable outcomes. Answer: 3 : 4

SILVER 2 points

4) A coin is tossed 6 times, find the probability of getting 2 tails. Leave your answer as a fraction. Process: You can do 6C2 to find the number of ways to get 2 tails, divided by the sample space of 26. Answer:15/64

5) How many 3-digit numbers larger than 600 can be formed from the digits 4, 5, 6, and 7 if repetition is not allowed? Process: The first number must be a 6 or 7, then you may use any of the 3 other numbers, than any of the 2 other available numbers. 2 x 3 x 2 = Answer:12

6) How many ways can you arrange the letters of “combination.” Process: 11! Divided by 2! x 2! x 2! because there are 3 sets of letters that are repeated twice. Answer:4,989,600

7) You are selecting a 4-person committee from the 50 Governors. There are 38 male Governors and 12 female Governors. How many different committees can be selected if you want to select 3 women and 1 man? Process: 12C3 x 38C1 = Answer:8,360

GOLD 3 points

8) Mr. and Mrs. Boyer have 4 children. What is the probability that their oldest and youngest child are girls? Hint: List out the sample space. Process: GGGG, GBBG, GBGG, GGBG. There are 4 favorable outcomes divided by a sample space of 24. Answer:4/16 or 1/4

9) Two dice are rolled. If you roll a sum greater than 9, you win $4. Otherwise, you lose $1. What is your mathematical expectation? Round to the nearest penny. Process:4,6 6, 45,5 5,6 6,5 and 6,6. The probability of rolling a sum greater than 9 is 6/36. Thus, the probability of the other outcomes is 30/36. (6/36)($4) + (30/36)(-$1) = Answer: -$0.17

10) Last year, the I.R.S. audited 2.3% of all tax returns. If a tax return is randomly selected, what are the odds in favor of it being audited? Process: Favorable : Unfavorable = 2.3 : 97.7 = Answer: 23:977

11) Twelve cans of soda consisting of 4 Pepsi, 3 Coke, 2 Root Beer, and 3 Seven-up are placed on a shelf. In how many different ways can this be done if cans of the same brand stay together? Process: Pepsi can be arranged in 4! ways. Coke can be arranged in 3! ways. Root Beer can be arranged in 2! ways. Seven-Up can be arranged in 3! ways. The different brands can be ordered in 4! ways. Multiply all of these together. Answer:41,472

12) You are selecting a 4-person committee from the 50 Governors. There are 38 male Governors and 12 female Governors. find the probability that the committee will consist of two males and two females. Put as a % rounded to the nearest hundredth. Process: 38C2 x 12C2 divided by 50C4 Answer:20.15%

Tiebreaker) You and 3 others are sitting in 4 chairs. You will not sit next to one of the other people. In how many ways can this be done. Answer: 12

HW • P. 231 #1-19 Odds • To study, look at this slideshow, past slideshows, the book, the chapter review, etc. • Winners: Every Other Odd • Test Tomorrow

Advanced Math Topics