Three identical coins are tossed together. What is the probability of obtaining :
all tails ?

Answer

To solve the problem of finding the probability of obtaining all tails when three identical coins are tossed, we can follow these steps:

### Step 1: Determine the Sample Space
When three coins are tossed, each coin can either land on heads (H) or tails (T). The total number of outcomes can be calculated as follows:

- Each coin has 2 possible outcomes (H or T).
- Therefore, for 3 coins, the total number of outcomes is \(2^3 = 8\).

The sample space (all possible outcomes) is:
1. HHH
2. HHT
3. HTH
4. HTT
5. THH
6. THT
7. TTH
8. TTT

### Step 2: Identify Favorable Outcomes
Next, we need to identify the favorable outcomes for the event we are interested in, which is obtaining all tails (TTT).

From the sample space, we can see that there is only **1 favorable outcome**:
- TTT

### Step 3: Calculate the Probability
The probability of an event is given by the formula:

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

Substituting the values we found:
- Number of Favorable Outcomes = 1 (TTT)
- Total Number of Outcomes = 8

Thus, the probability of obtaining all tails is:

\[ \text{Probability} = \frac{1}{8} \]

### Final Answer
The probability of obtaining all tails when three identical coins are tossed is \(\frac{1}{8}\).

---