Three identical coins are tossed together. What is the probabilit of obtaining:
no head?

Answer

To find the probability of obtaining no heads when three identical coins are tossed, we can follow these steps:

### Step 1: Determine the total number of outcomes
When three coins are tossed, each coin has 2 possible outcomes: heads (H) or tails (T). Therefore, the total number of outcomes when tossing three coins can be calculated as:
\[ \text{Total outcomes} = 2^n \]
where \( n \) is the number of coins. In this case, \( n = 3 \):
\[ \text{Total outcomes} = 2^3 = 8 \]

### Step 2: List all possible outcomes
The possible outcomes when tossing three coins are:
1. HHH (3 heads)
2. HHT (2 heads, 1 tail)
3. HTH (2 heads, 1 tail)
4. THH (2 heads, 1 tail)
5. HTT (1 head, 2 tails)
6. THT (1 head, 2 tails)
7. TTH (1 head, 2 tails)
8. TTT (0 heads, 3 tails)

### Step 3: Identify favorable outcomes for no heads
We need to find the outcomes that result in no heads. From the list above, the only outcome that has no heads is:
- TTT (0 heads)

Thus, the number of favorable outcomes for obtaining no heads is:
\[ \text{Favorable outcomes} = 1 \]

### Step 4: Calculate the probability
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} \]
Substituting the values we found:
\[ \text{Probability of no heads} = \frac{1}{8} \]

### Final Answer
The probability of obtaining no heads when three identical coins are tossed is:
\[ \frac{1}{8} \]

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