Three identical coins are tossed together. What is the probability of obtaining :
exactly one head ?

Answer

To find the probability of obtaining exactly one head 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 when tossing three coins can be calculated as:
\[ \text{Total Outcomes} = 2^n \]
where \( n \) is the number of coins. Here, \( n = 3 \):
\[ \text{Total Outcomes} = 2^3 = 8 \]

The sample space (all possible outcomes) is:
- HHH
- HHT
- HTH
- HTT
- THH
- THT
- TTH
- TTT

### Step 2: Identify Favorable Outcomes
Next, we need to identify the outcomes that have exactly one head. The outcomes with exactly one head are:
- HTT
- THT
- TTH

Thus, there are 3 favorable outcomes.

### Step 3: Calculate the Probability
The probability \( P \) of an event is given by the formula:
\[ P(\text{Event}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]
Substituting the values we found:
\[ P(\text{Exactly one head}) = \frac{3}{8} \]

### Conclusion
The probability of obtaining exactly one head when three identical coins are tossed is:
\[ \frac{3}{8} \]

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