A penny, a nickel, a dime, and a quarter are placed in a box. The coins are mixed up and two coins are picked, one at a time. Each time a coin is picked it is NOT put back in the bag. Create a tree diagram to show all of the possible totals.
To create a tree diagram showing all the possible totals, we start by listing all the coins in the first column. Then, for each coin, we list all the possible options for the second coin in the row below.
Let's begin by considering the first coin selected:
1. Penny:
- Nickel:
- Total: 6 cents (penny + nickel)
- Dime:
- Total: 11 cents (penny + dime)
- Quarter:
- Total: 26 cents (penny + quarter)
2. Nickel:
- Penny:
- Total: 6 cents (nickel + penny)
- Dime:
- Total: 15 cents (nickel + dime)
- Quarter:
- Total: 30 cents (nickel + quarter)
3. Dime:
- Penny:
- Total: 11 cents (dime + penny)
- Nickel:
- Total: 15 cents (dime + nickel)
- Quarter:
- Total: 35 cents (dime + quarter)
4. Quarter:
- Penny:
- Total: 26 cents (quarter + penny)
- Nickel:
- Total: 30 cents (quarter + nickel)
- Dime:
- Total: 35 cents (quarter + dime)
This tree diagram represents all the possible totals when two coins are picked from the box, one at a time and not put back in the box.