A fair coin is tossed repeatedly. The probability of getting a result in the fifth toss different from those obtained in the first four tosses is:

Options

A. A. `1//2`
B. B. `1//32`
C. C. `31//32`
D. D. `1//16`

Answer

To solve the problem of finding the probability of getting a result in the fifth toss different from those obtained in the first four tosses when tossing a fair coin, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Coin Tosses:**
A fair coin has two possible outcomes for each toss: Heads (H) or Tails (T). When we toss the coin 5 times, each toss is independent of the others.

2. **Determining the Sample Space:**
The total number of outcomes when tossing a coin 5 times can be calculated as:
\[ \text{Total Outcomes} = 2^5 = 32 \]
This is because each of the 5 tosses has 2 possible outcomes.

3. **Identifying Favorable Outcomes:**
We need to find the probability that the result of the fifth toss is different from the results of the first four tosses.
- If the first four tosses are all Heads (HHHH), the fifth toss must be Tails (T) to be different.
- Conversely, if the first four tosses are all Tails (TTTT), the fifth toss must be Heads (H) to be different.
- Therefore, there are only 2 favorable outcomes:
- HHHH followed by T
- TTTT followed by H

4. **Calculating the Probability:**
The probability of the fifth toss being different from the first four tosses is given by the ratio of favorable outcomes to total outcomes:
\[ P(\text{5th toss different}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} = \frac{2}{32} = \frac{1}{16} \]

5. **Conclusion:**
The probability of getting a result in the fifth toss different from those obtained in the first four tosses is:
\[ \frac{1}{16} \]