You toss a coin 5 times in a row. If a tree diagram were used to illustrate the possible outcomes of this experiment, how many branches would it have?

When you toss a coin 5 times, each toss has 2 possible outcomes: heads (H) or tails (T).

A tree diagram starts with a single branch and then splits into 2 branches for each possible outcome at every step (each toss).

To calculate the total number of branches in the tree diagram after 5 tosses:

- After the 1st toss: 2 branches
- After the 2nd toss: \(2 \times 2 = 4\) branches
- After the 3rd toss: \(4 \times 2 = 8\) branches
- After the 4th toss: \(8 \times 2 = 16\) branches
- After the 5th toss: \(16 \times 2 = 32\) branches

So, the tree diagram would have **32 branches** after 5 tosses.

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

Here are 5 related questions you might find interesting:
1. How many different sequences of heads and tails can occur if a coin is tossed 5 times?
2. If a coin is tossed 5 times, what is the probability of getting exactly 3 heads?
3. How does the number of branches change if the coin is tossed 6 times?
4. How many branches would there be in a tree diagram if the coin is tossed 10 times?
5. What would the tree diagram look like if the coin had 3 possible outcomes instead of 2?

**Tip:** The number of branches in a tree diagram grows exponentially with the number of events (in this case, coin tosses).

Explore how to illustrate the possible outcomes of tossing a coin 5 times using a tree diagram. Learn about the exponential growth of branches with each toss and related probability concepts. Suitable for students in Grades 7-9.

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