There is a `(1)/(2)` probability that a certain coin will turn up heads on any given toss. What is the probability that two tosses of the coin will yields heads both times?

Answer

To solve the problem of finding the probability that two tosses of a coin will yield heads both times, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Probability of Heads**:
- The probability of getting heads on a single toss of the coin is given as \( P(H) = \frac{1}{2} \).

2. **Identify the Events**:
- We are interested in two independent events:
- The first toss resulting in heads.
- The second toss also resulting in heads.

3. **Calculate the Probability for Two Tosses**:
- Since the tosses are independent, the probability of both events occurring (both tosses resulting in heads) can be calculated by multiplying the probabilities of each individual event:
\[ P(\text{Both Heads}) = P(H \text{ on 1st toss}) \times P(H \text{ on 2nd toss}) \]
- Substituting the known probabilities:
\[ P(\text{Both Heads}) = \frac{1}{2} \times \frac{1}{2} \]

4. **Perform the Multiplication**:
- Calculate the product:
\[ P(\text{Both Heads}) = \frac{1}{4} \]

5. **Conclusion**:
- Therefore, the probability that two tosses of the coin will yield heads both times is \( \frac{1}{4} \).

### Final Answer:
The probability that both tosses will result in heads is \( \frac{1}{4} \).

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