A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of head appearing on fifth toss is equal to

Options

A. `1/2`
B. `(1)/(32)`
C. `(31)/(32)`
D. `(1)/(5)`

Answer

To solve the problem, we need to determine the probability of getting a head on the fifth toss of a fair coin after observing tails on the first four tosses.

### Step-by-step Solution:

1. **Understanding the Coin Toss**: A fair coin has two possible outcomes: heads (H) and tails (T). The probability of getting heads (P(H)) or tails (P(T)) on any single toss is equal, specifically:
\[ P(H) = P(T) = \frac{1}{2} \]

2. **Independence of Events**: The outcome of each toss of the coin is independent of the previous tosses. This means that the result of the fifth toss does not depend on the results of the first four tosses.

3. **Calculating the Probability of the Fifth Toss**: Since the fifth toss is independent, we can directly calculate the probability of getting heads on the fifth toss:
\[ P(\text{Head on 5th toss}) = \frac{1}{2} \]

4. **Conclusion**: Therefore, the probability of getting a head on the fifth toss, regardless of the outcomes of the first four tosses, is:
\[ \boxed{\frac{1}{2}} \]