Three coins are tossed together. What is the probability that first shows head, second shows tail and third shows head?

Answer

To solve the problem of finding the probability that the first coin shows heads, the second coin shows tails, and the third coin shows heads when three coins are tossed, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Outcomes for Each Coin:**
- Each coin has two possible outcomes: Heads (H) or Tails (T).
- Therefore, the outcomes for each coin can be represented as:
- Coin 1: H or T
- Coin 2: H or T
- Coin 3: H or T

2. **Calculate the Total Number of Outcomes:**
- Since there are 3 coins and each coin has 2 outcomes, the total number of outcomes when tossing 3 coins is calculated as:
\[ \text{Total Outcomes} = 2^3 = 8 \]

3. **Determine the Desired Outcome:**
- We want to find the probability of the specific outcome: Coin 1 shows Heads (H), Coin 2 shows Tails (T), and Coin 3 shows Heads (H).
- This specific outcome can be represented as HTH.

4. **Calculate the Probability of the Desired Outcome:**
- The probability of each individual outcome (H or T) for a fair coin is \( \frac{1}{2} \).
- Therefore, the probability of getting HTH is calculated by multiplying the probabilities of each coin:
\[ P(\text{HTH}) = P(H) \times P(T) \times P(H) = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8} \]

5. **Conclusion:**
- The probability that the first coin shows heads, the second coin shows tails, and the third coin shows heads is \( \frac{1}{8} \).

### Final Answer:
The probability that the first coin shows heads, the second coin shows tails, and the third coin shows heads is \( \frac{1}{8} \).