A coin is tossed five times. What is the porbability that the fourth toss would turn a head?

Options

A. `1/(._5P_5)`
B. `1/(._5P_9)`
C. `1/2`
D. `1/(2!)`

Answer

To solve the problem of finding the probability that the fourth toss of a coin will result in heads when a coin is tossed five times, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the scenario**: We are tossing a coin five times. Each toss is independent of the others, meaning the outcome of one toss does not affect the others.

2. **Identify the outcomes for a single toss**: When tossing a coin, there are two possible outcomes: heads (H) or tails (T). The probability of getting heads (P(H)) is 1/2, and the probability of getting tails (P(T)) is also 1/2.

3. **Focus on the fourth toss**: We need to find the probability that the fourth toss results in heads. Since each toss is independent, the outcome of the fourth toss does not depend on the results of the first three or the fifth toss.

4. **Calculate the probability for the fourth toss**: The probability that the fourth toss results in heads is simply the probability of getting heads in any single toss, which is:
\[ P(\text{4th toss is H}) = \frac{1}{2} \]

5. **Conclusion**: Therefore, the probability that the fourth toss would turn out to be heads is \( \frac{1}{2} \).

### Final Answer:
The probability that the fourth toss would turn a head is \( \frac{1}{2} \).

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