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Probability Review

Probability Review. The Lottery. Many people love to play the lottery in hopes of winning a lot of money. However, few people think about their odds of winning.

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Probability Review

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  1. Probability Review

  2. The Lottery Many people love to play the lottery in hopes of winning a lot of money. However, few people think about their odds of winning. The basic lottery game has players choose five numbers and write them on a ticket. Then, five numbers are drawn randomly and only a ticket that matches all five numbers exactly will win. You task is to find out exactly what your chances are of picking all five numbers exactly. Let’s say that you have to pick five numbers from 1-25. Use what you know about probability to calculate this one. You will also need to use the calculator provided. How good are your chances of winning? Do you think that buying a lottery ticket is a good use of your money? Why or why not?

  3. How Safe is the Safe? Mr. Random was a nervous fellow. He was afraid that someone would break into his house and steal his valuable coin collection. So, he decided to buy a safe to keep his collection in. Mr. Random had to decide on the combination for his safe’s lock. The combination had to be composed of three numbers (0-9). Mr. Random wanted to create the safest combination possible. Mr. Random could choose to either repeat numbers or not. If he chose to not repeat numbers, how many different combinations could he use? If he chose to repeat numbers, how many different combinations could he use? Should Mr. Random choose to repeat of not repeat numbers for his combination? Why?

  4. Sock It To Me! Susy had the following kinds of socks in her drawer: 2 yellow socks with smiley faces 2 black socks with moons 2 blue socks with clouds 2 red socks with hearts 2 rainbow-colored Susy Stockings was proud of her crazy sock collection. She loved to show them off every day at school. One morning, Susy woke up and her electricity was off. It was a power outage. She had to get dressed in the dark and could not see to match up her socks. Susy was not very neat and always just threw her socks into her drawer without matching them up. She panicked. She could not wear socks that didn’t match to school. Use the information at the right to help decide the minimum number of socks Susy would have to pull out of her drawer before she would be certain to have at least one matching pair.

  5. Mixed-Up Keys Mr. Oops works at a local hotel. One busy day, Mr. Oops had to take eight different guests to eight different rooms at the same time. The problem is that the labels for the keys have faded, and Mr. Oops has no idea which key fits which room door. Your task is to figure out the most tries that it would take Mr. Oops to find the right key for each of the eight rooms. Assume that once he finds a key for one room, he marks it. Extra Challenge: What is the probability that Mr. Oops will open all eight doors on the first try?

  6. Movie Marble Madness Mike and Maria go to the Funplex Movie Theatre to see Attack of the Giant Math Teacher. When they arrive, they notice that there is a special contest going on. There are two boxes sitting on the counter. Box A has one green marble hidden amongst nine red marbles. Box B has 10 green marbles hidden amongst 90 red marbles. Each person is blindfolded and can pick one marble from either Box A or Box B. Anyone who picks a green marble wins a free popcorn. Mike decides to pick from Box A. Maria decides to pick from Box B. Which person has the better chance of winning the popcorn? Explain your answer by giving the probability for Mike and Maria to win the popcorn.

  7. Do You Want Fries With That? McDoogles Restaurant wants to add more variety to its menu. However, the manager at McDoogles is afraid that giving the customer too many choices will slow down the lines. He hires you to figure out how many different meal combinations can be ordered from their menu. Each meal-deal includes a choice of: - a hamburger or cheeseburger - fries, onion rings, or fruit - pop, juice, or chocolate or white milk How many different combinations of meals can be ordered?

  8. What Are Your Chances? Miss Weaver decides to give away her car to someone in your class. She is going to do this by simply drawing one of her students’ names out of a hat. If everyone’s name is put in the hat one time, what is your chance of winning her car? What if everyone gets to put his/her name in the hat twice? What is your chance of winning now? Are your chances of winning better now that before? Why or why not? What if she had two cars to give away – one for a boy and one for a girl. She put all the girls’ names in one hat and all the boys’ names in another. What are your chances of winning now? Are they better than before? Why or why not?

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