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. Candy Confusion Your mom brings home the candy bars pictured. Unfortunately, you and your four siblings all want the Snickers, but there is only one. Mom decides to place all the candy bars into a bag and let each of you draw one out, and what you draw is what you get. If your big sister goes first, what is her probability of pulling out the Snickers? If she pulls out the PayDay, what is the next person’s probability of getting the Snickers? Your little brother goes next and pulls out the Almond Joy. What is your probability of getting the Snickers bar if you draw next? Is this a fair way of deciding who gets the Snickers? Explain your thinking.

4. 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?

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. Sock It To Me! 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. 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