Five coins are tossed at a time. Then, the probability of obtaining atleast one tail is

Options

A. `31/32`
B. `1/32`
C. `1/5`
D. `5/32`

Answer

To solve the problem of finding the probability of obtaining at least one tail when tossing five coins, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Total Outcomes**:
When tossing a coin, there are 2 possible outcomes: Heads (H) or Tails (T). Therefore, when tossing 5 coins, the total number of outcomes can be calculated as:
\[ \text{Total Outcomes} = 2^5 = 32 \]

2. **Calculate the Probability of the Complement Event**:
Instead of calculating the probability of getting at least one tail directly, it is easier to calculate the probability of the complement event, which is getting no tails (i.e., all heads). There is only one way to get all heads (HHHHH):
\[ \text{Probability of getting all heads} = \frac{1}{32} \]

3. **Calculate the Probability of Getting At Least One Tail**:
The probability of getting at least one tail is the complement of the probability of getting all heads. Therefore, we can find it as follows:
\[ P(\text{At least one tail}) = 1 - P(\text{All heads}) = 1 - \frac{1}{32} = \frac{31}{32} \]

4. **Final Answer**:
Thus, the probability of obtaining at least one tail when tossing five coins is:
\[ P(\text{At least one tail}) = \frac{31}{32} \]