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The problem in the image involves calculating the probability of getting at most 3 heads when five fair coins are tossed. Here's a breakdown of the solution provided:

### Problem
We are given **5 fair coins** and need to find the **probability of getting at most 3 heads**.

### Solution Process
The solution starts by calculating this probability using complementary counting, i.e., subtracting the probability of getting **at least 4 heads** from 1.

**Step 1: Use Complementary Counting**
\[
\text{Probability of at most 3 heads} = 1 - \text{Probability of at least 4 heads}
\]
Thus,
\[
\text{Probability of at least 4 heads} = \text{Probability of getting 4 heads} + \text{Probability of getting 5 heads}
\]

**Step 2: Calculate the Probability of Getting 4 Heads**
The probability of getting exactly 4 heads is calculated using the binomial coefficient, as it represents the number of ways to choose 4 heads out of 5 coins. The probability for each outcome (head or tail) is \( \frac{1}{2} \), so:
\[
\text{Probability of 4 heads} = \binom{5}{4} \times \left(\frac{1}{2}\right)^5 = 5 \times \frac{1}{32} = \frac{5}{32}
\]

**Step 3: Calculate the Probability of Getting 5 Heads**
Similarly, the probability of getting exactly 5 heads is:
\[
\text{Probability of 5 heads} = \binom{5}{5} \times \left(\frac{1}{2}\right)^5 = 1 \times \frac{1}{32} = \frac{1}{32}
\]

**Step 4: Add These Probabilities**
Now, the total probability of getting at least 4 heads is:
\[
\frac{5}{32} + \frac{1}{32} = \frac{6}{32}
\]

**Step 5: Subtract from 1**
Finally, subtract this result from 1 to find the probability of getting at most 3 heads:
\[
1 - \frac{6}{32} = \frac{32}{32} - \frac{6}{32} = \frac{26}{32} = \frac{13}{16}
\]

### Final Answer
The probability of getting at most 3 heads is \( \frac{13}{16} \).

---

Would you like more details on any of the steps, or do you have any further questions?

Here are some related questions to explore:

1. How do binomial coefficients work in probability?
2. What is the difference between using complementary counting and direct counting?
3. How do we generalize this method for any number of coins?
4. What is the binomial probability formula?
5. How does the probability change if we increase the number of coins?

**Tip**: When solving probability problems involving multiple independent events, always consider using complementary counting if the direct calculation seems difficult.

Five fair coins are tossed together. Find the probability of getting at most 3 heads.

Find the probability of getting at most 3 heads when tossing 5 fair coins using binomial probability and complementary counting. This solution covers key concepts such as binomial distribution and the binomial theorem. Suitable for high school students in grades 10-12.

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