To draw a tree diagram for this game, we need to account for all the possible outcomes from flipping the coin and rolling the dice. Here's how we can break it down:

1. Coin Flip: There are two possible outcomes: Head (H) or Tail (T).
2. Dice Roll: For each coin flip outcome, there are 6 possible dice outcomes: 1, 2, 3, 4, 5, or 6.

Thus, the total number of outcomes is $2 \times 6 = 12$ possible combinations.

Steps to create the tree diagram:

• Start with a branch for the coin flip, which splits into two: H (Head) and T (Tail).
• For each coin flip outcome, branch out into 6 more branches representing the dice rolls: 1, 2, 3, 4, 5, and 6.

The game rules are as follows:

• Brenda wins if a head is flipped and a number above 2 is rolled.
• Hannah wins if a tail is flipped and a number 2 or more is rolled.

Now, I'll describe how the tree diagram would look:

1. From the starting point, draw a branch labeled H (Head) and another branch labeled T (Tail).
2. Under each of these, create 6 branches corresponding to the dice outcomes: 1, 2, 3, 4, 5, 6.
   • For H (Head): label the branches 1, 2, 3, 4, 5, 6.
   • For T (Tail): label the branches 1, 2, 3, 4, 5, 6.

Outcome Summary for the Tree:

• H (Head) → 1: Not Brenda’s win.

• H (Head) → 2: Not Brenda’s win.

• H (Head) → 3: Brenda wins.

• H (Head) → 4: Brenda wins.

• H (Head) → 5: Brenda wins.

• H (Head) → 6: Brenda wins.

• T (Tail) → 1: Not Hannah’s win.

• T (Tail) → 2: Hannah wins.

• T (Tail) → 3: Hannah wins.

• T (Tail) → 4: Hannah wins.

• T (Tail) → 5: Hannah wins.

• T (Tail) → 6: Hannah wins.

Visual Representation:

plaintextCopy code
                         Start
                         /   \
                    H(Head) T(Tail)
                     / \      /  |  |  |  |  \
                   1   2    1   2  3  4  5  6
                      |      |   |  |  |  |  |
                  (No)  (No) (No) (Yes) (Yes) (Yes) (Yes) 
                                (Yes) (Yes) (Yes) (Yes)

• (No) means neither player wins.
• (Yes) means the corresponding player wins (Brenda or Hannah).

Would you like more details on the rules or any other clarification?

Here are some related questions:

1. What is the probability that Hannah wins the game?
2. How can you calculate the odds of Brenda winning the game?
3. What if the dice had only 4 sides instead of 6? How would the tree change?
4. What’s the probability that either player wins the game in this scenario?
5. Can this game be modified so that both players have an equal chance of winning?

Tip: Always break down the problem into smaller steps, like splitting coin flips and dice rolls into branches in a tree diagram, to better understand the possible outcomes.