https://file.aiquickdraw.com/mathbot/file/173440512306254jzawhh.jpg

The problem in the image translates to:

**"A fair coin is tossed three times. Find the expected number of heads."**

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### Solution:

To solve this, we use the properties of expected value:

1. **Probability of Heads**:  
   Since the coin is fair, the probability of getting a head (\( H \)) on any single toss is:  
   \[
   P(H) = \frac{1}{2}.
   \]

2. **Expected Value of One Toss**:  
   Let \( X_i \) represent the outcome of the \( i \)-th toss. Define \( X_i = 1 \) if a head appears and \( X_i = 0 \) otherwise.  
   The expected value of \( X_i \) is:  
   \[
   E(X_i) = 1 \cdot P(H) + 0 \cdot P(T) = \frac{1}{2}.
   \]

3. **Sum of Tosses**:  
   Let \( X \) represent the total number of heads in 3 tosses:  
   \[
   X = X_1 + X_2 + X_3.
   \]
   By the **linearity of expectation** (the expectation of a sum is the sum of expectations), we get:  
   \[
   E(X) = E(X_1) + E(X_2) + E(X_3).
   \]

   Substituting \( E(X_i) = \frac{1}{2} \) for each toss:  
   \[
   E(X) = \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = \frac{3}{2}.
   \]

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### Final Answer:
The expected number of heads (or "герб" in Russian) when tossing a fair coin 3 times is:  
\[
\boxed{1.5}
\]

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Would you like further details on any part of the solution? Here are 5 related questions for practice:

1. What is the expected number of heads if the coin is tossed \( n \) times?
2. If the coin is biased such that \( P(H) = 0.6 \), what is the expected number of heads in 3 tosses?
3. What is the variance of the number of heads in 3 tosses of a fair coin?
4. How does the expected value change if the coin is tossed 5 times instead of 3?
5. What is the probability of getting exactly 2 heads in 3 tosses?

**Tip**: The linearity of expectation holds even when random variables are not independent!

Трижды подбрасывается правильная монета. Найдите математическое ожидание количества выпадений герба.

Find the expected number of heads when tossing a fair coin 3 times. Using probability concepts and linearity of expectation, we calculate that the expected value is 1.5. This problem is suitable for high school students studying probability.

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