If three unbiased coins are tossed, then probability of getting at most two tails is

Options

A. `(1)/(8)`
B. `(1)/(2)`
C. `(5)/(8)`
D. `(7)/(8)`

Answer

To find the probability of getting at most two tails when tossing three unbiased coins, we can follow these steps:

### Step 1: Identify the total number of outcomes
When tossing three coins, each coin can either show heads (H) or tails (T). Therefore, the total number of outcomes when tossing three coins can be calculated as follows:

\[ \text{Total Outcomes} = 2^n \]
where \( n \) is the number of coins. Here, \( n = 3 \).

\[ \text{Total Outcomes} = 2^3 = 8 \]

### Step 2: List all possible outcomes
The possible outcomes when tossing three coins are:
1. HHH
2. HHT
3. HTH
4. THH
5. HTT
6. THT
7. TTH
8. TTT

### Step 3: Identify favorable outcomes for at most 2 tails
We need to find the outcomes that have at most 2 tails. This includes outcomes with:
- 0 tails
- 1 tail
- 2 tails

The outcomes that fit this criterion are:
1. HHH (0 tails)
2. HHT (1 tail)
3. HTH (1 tail)
4. THH (1 tail)
5. HTT (2 tails)
6. THT (2 tails)
7. TTH (2 tails)

Thus, the favorable outcomes are:
- HHH
- HHT
- HTH
- THH
- HTT
- THT
- TTH

### Step 4: Count the favorable outcomes
The number of favorable outcomes is 7.

### Step 5: Calculate the probability
The probability of getting at most 2 tails is given by the formula:

\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]

Substituting the values we found:

\[ \text{Probability} = \frac{7}{8} \]

### Conclusion
The probability of getting at most 2 tails when tossing three unbiased coins is \( \frac{7}{8} \).

---