The image contains a problem asking for a tree diagram showing all possible results when three fair coins are tossed, and the user is asked to choose the correct tree diagram from three options (A, B, or C).

Let’s break down the problem:

Possible Outcomes for Three Coin Tosses:

• Each coin can land either Heads (H) or Tails (T).
• For three coins, the total number of possible outcomes is $2^3 = 8$.

Listing All Possible Outcomes:

• HHH (all heads)
• HHT
• HTH
• HTT
• THH
• THT
• TTH
• TTT (all tails)

This is consistent with a typical binary tree structure. Each level in the tree corresponds to a coin toss (with two branches per toss representing heads or tails).

Analyzing the Diagrams:

• The diagram needs to represent 8 total outcomes at the end of 3 levels.

• The order and arrangement should reflect all possible combinations of heads and tails.

• Option A: This shows a binary tree with 8 distinct outcomes after 3 coin tosses (e.g., HHH, HHT, HTT, etc.).

• Option B and C: These trees have inconsistencies in how they organize the results, such as repeating the same outcomes or not covering all possible ones.

Conclusion:

The correct tree diagram representing all 8 outcomes is Option A, as it accurately shows the branching of each coin toss leading to all 8 unique results.

Would you like more details or have any other questions about this?

Here are 5 related questions:

1. How many possible outcomes are there when 4 fair coins are tossed?
2. What is the probability of getting exactly two heads when tossing three coins?
3. Can you represent the outcomes of tossing two coins using a tree diagram?
4. How would the tree diagram change if you flipped a coin twice instead of three times?
5. What is the probability of getting more than two tails when tossing three coins?

Tip: When dealing with multiple independent events, tree diagrams help visualize all possible outcomes step by step, making it easier to compute probabilities.