1. Suppose you roll 5 dice in a certain game. You need at least one of those dice to be a five or a six. What is the probability this happens?
2. Suppose you are playing a game where you roll a die 5 times. If any of those rolls come out to be a five or a six, then you lose. What is the probability you lose?
3. The Mega Million lottery has odds around 1 in 300 million. Suppose you buy 1,000 tickets.

a. A lot of people would say that your odds of winning are (1/300000000)^1000. Explain why this answer is too small to be right?

b. Thinking of each ticket as giving you a separate chance to win, what is the correct answer for your odds winning?

1. An investment requires you to invest $500,000. There is a 1% chance that it will grow to $75,000,000 and a 99% chance you will lose all your money.

a. Compute the expected value.

b. If you got 255,500, then your answer is wrong: go back and fix it. Someone getting the answer would likely be doing (750000000(0.01)+(-500000)(0.99). What is wrong about doing that?

c. Assuming that $500,000 is your entire life savings, which took you 30 years to work to save, is this is a smart investment for you? Why or why not?

d. What about a large investment company that makes this investment thousands of times per year? Is this a wise investment for them? Explain.