Flipping Coins

Fred and Ethel are having a conversation about flipping coins.

1. Ethel asks Fred if he knows the chance of getting 2 heads if you flip 2 coins. Fred says, "Well, you could get 2 heads, or you could get 1 head and 1 tail, or you could get 2 tails. So, I think the chance of getting 2 heads is 1/3." What do you think? Show your work.

2. Fred asks Ethel if she knows the chance of getting 2 heads if you flip 3 coins. What would be your answer to that question? Show your work.

The One-and-One Problem

Sometimes during a basketball game, when a player is fouled, she gets to shoot a "one-and-one." This means that the player shoots a foul shot or "free throw." If the player misses, that is it. If the player makes the first shot, she gets one more. Each shot made is worth one point.

Fred is a player who makes about 60 percent of the free throws he attempts.

3. How many points is Fred most likely to score in a one-and-one situation? Show your work.

4. Over the course of many one-and-one situations, what is the average number of points Fred will score? Show your work.

The Payment Plan Problem

You have been paying a delivery service $5 per week to make regular deliveries to your house. One week, just to make things interesting, you offer the service a new payment plan. Each week, you will allow the delivery person to reach into a paper bag and pull out two bills. The bag will contain one $10 bill and five $1 bills.

5.Which method makes the most money over the course of many weeks?Show your work.

A Dice Game

Fred and Ethel play a dice game. They take turns rolling a pair of dice. For each roll of the dice, if the sum of the two numbers is a multiple of 3, then Fred wins $3 from Ethel. If the sum is not a multiple of 3, then Ethel wins $2 from Fred.

6. What is the probability that Fred will win?

7.What is the probability that Ethel will win?

8.Who will win more money?