When three coins are tossed together, the probability that all coins have the same face is-

Options

A. `1/4`
B. `1/6`
C. `1/3`
D. None of these

Answer

To find the probability that all three coins show the same face when tossed together, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Total Possible Outcomes:**
When a coin is tossed, it can either land on heads (H) or tails (T). For three coins tossed together, we can calculate the total possible outcomes.
- For the first coin, there are 2 possibilities (H or T).
- For the second coin, there are also 2 possibilities (H or T).
- For the third coin, there are again 2 possibilities (H or T).

Therefore, the total number of possible outcomes when tossing three coins is:
\[ 2 \times 2 \times 2 = 8 \]

2. **Identify Desired Outcomes:**
We need to determine the outcomes where all three coins show the same face. The two scenarios where this occurs are:
- All coins show heads (HHH)
- All coins show tails (TTT)

Thus, there are a total of 2 desired outcomes.

3. **Calculate Probability:**
The probability (P) is calculated using the formula:
\[ P = \frac{\text{Desired Outcomes}}{\text{Total Possible Outcomes}} \]
Substituting the values we found:
\[ P = \frac{2}{8} = \frac{1}{4} \]

### Final Answer:
The probability that all coins have the same face is \(\frac{1}{4}\).

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