The Math Genius and the Plane Vernon is planning a trip over winter break to Salt Lake City, Utah to see his family. He is excited about traveling by plane, but he has heard stories about people’s luggage being delayed, lost and stolen. Vernon has also heard many stories about planes not meeting their departure and arrival times. Since this is his first trip by plane he wants to sit by a window. He decides to do a little research to find out how to best avoid problems with his luggage and to find out his chances of being on time problems 1. First he decides to work on the luggage problem. Taya, one of his friends, tells him he should purchase luggage that is colorful rather than the standard black or gray. Taya believes that other passengers simply claim the wrong bags because so many look alike. Vernon makes a trip to the mall to shop for new luggage. What he finds are suit bags, duffle bags, weekender bags, carryons, totes, and backpacks. He finds that each of these bags comes in black, brown, gray, red, and paisley. The luggage can be wheeled or not. The luggage can be softsided or hardsided. How many different pieces of luggage can Vernon purchased based on the information above. Show all work.
2. Wyn, another of his friends, tells him there is no need to purchase new colorful luggage. Instead he should embellish the black luggage his has with colorful handles and straps. Vernon thinks about his black suitcase and wonders if he should add red or blue handles. Should he add yellow or green straps? Should he add both straps and handles? How many different pieces of luggage could Vernon create using the information above? Be careful here, Vernon can add as many or as few embellishments as he would like.
3. Vernon’s younger sister, Aisha, sees Vernon’s calculations and asks what he is doing. Vernon explains the fundamental counting principle to her. Aisha doesn’t understand what Vernon is telling her, but she tells him she can find the outcomes using a drawing. What is the mathematical name of Aisha’s drawing? Make the drawing below for #1 or #2 above.
4. Vernon has finally settled his luggage problem and gets ready to choose a seat on the plane. The MD80 seats 144 passengers; 12 in first class, 20 business class and the rest in coach. Vernon is seated in the coach section and wants you to help him find how many different seat configurations are possible. He knows that this is a huge number for coach, but the number in first class can be calculated without too much trouble. Find the seat configurations for first class. Show all work and explain the process.
5. Of the 20 people in business class 8 are women and 12 are men. Six of the women and ¾ of the men are dressed in business attire. There rest are dressed casually. If Vernon were to select at random what is the probability of selecting a someone in business attire or a woman?
6. Vernon begins to research the probability of his plane departing on time. He goes to the internet and looks up SkyV airlines and checks the data. He finds the following table
21 Depart Monday Arrive Depart Tuesday Arrive Depart Wednesday Arrive Depart Thursday Arrive Depart Friday Arrive Depart Saturday Arrive Depart Sunday Arrive
on time on time late late on time on time late late on time late late late on time on time
Flights #'s 672 394 501 late late on time late late late on time late late on time late late on time on time on time on time on time on time late on time late late on time late on time late on time on time late on time on time on time on time on time late on time on time on time on time on time late on time
Using the table find the following probabilities. (Show all calculations and explain how you selected the numbers and why you performed the chosen operation) a) departing on time
b) Arriving on time
c) departing and arriving on time
d) departing or arriving on time 7. Vernon has finally arrived at the airport for his trip. While standing in the TSA screening line he notices some passengers are asked to take off their shoes as they go through the screening process, while some have some type of pass card that allows them to move through the screening process more quickly. Vernon asks a gentleman next to him what this card is all about. Once the information is given, Vernon’s math mind begins to calculate. If there are 2 letters that are case sensitive followed by 3 numbers, and finally followed by 1 vowel that is not case sensitive, how many combinations are possible for the pass cards? Show all work and calculations.
Vernon boards his plane and gets ready for departure. He is pleasantly surprised to find himself seated next to another ‘math genius’ and they engage in several games to pass the time. See if you are as accurate as Vernon in calculating his winnings. 8. Zeroun and Vernon begin by playing backgammon. Zeroun rolls double 6’s. What is Vernon’s chance of rolling double 6’s?
9. Next the two new friends engage in their own version of the card game, Blackjack. The hand with the highest total wins as long as it doesn't exceed 21; a hand with a higher total than 21 is said to bust or too many. Cards 2 through 10 are worth their face value,
and face cards (jack, queen, king) are all worth 10. An ace's value is 11 unless this would cause the player to bust, in which case it is worth 1.) Vernon draws a King of hearts, and a 5 of spades. Zeroun has an Ace of Clubs and an 8 of diamonds. Find: a) Vernon’s probability of drawing a 5 of diamonds. b) Zeroun’s probability of drawing a 3 of clubs or a 3 of hearts. 10. After tiring of the card games they move on to a game of dice. For the first game they use two dice and sum the numbers. If the sum is 2, 4, 6,8,10 then Vernon wins. If the sum is 3, 5,7,9,11,12 then Zeroun wins. Is this a fair game? Explain. Include a table of outcomes as part of your answer. If the game is unfair, how can the rules be changed to make a fair game.
11. Zeroun is a creative person and creates the next game using a coin and one die. For this game, if the coin lands on heads and the die on an even number Vernon wins. If the coin lands on tails and an odd number Zeroun wins. If the coin is heads and odd, Vernon wins. If the coin is tails and even Zeroun wins. Vernon is unsure if he should play this game. He is not sure it is fair. What advice would you give Vernon? Include charts/diagrams to convince Vernon of the correct decision.
12. As the plane descends for landing, the two new friends have a disagreement about the outcomes of tossing three coins at one time. Vernon says there are 6 outcomes, and Zeroun says there are 8 outcomes. How does Vernon come up with an answer of 6? How does Zeroun come up with an answer of 8? Which one is correct? Explain.