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

Answer

To find the probability of obtaining at least 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 show a Head (H) or a Tail (T). The total outcomes can be represented as follows:

- HHH
- HHT
- HTH
- HTT
- THH
- THT
- TTH
- TTT

Thus, the sample space (S) consists of 8 possible outcomes:
\[ S = \{ HHH, HHT, HTH, HTT, THH, THT, TTH, TTT \} \]

### Step 2: Count the Total Outcomes
From the sample space, we can see that there are a total of 8 outcomes.

### Step 3: Identify Favorable Outcomes
Next, we need to find the outcomes that have at least one head. The favorable outcomes are:
- HHH
- HHT
- HTH
- HTT
- THH
- THT
- TTH

Counting these, we find that there are 7 outcomes that contain at least one head.

### Step 4: 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:
\[ P(\text{at least one head}) = \frac{7}{8} \]

### Final Answer
Thus, the probability of obtaining at least one head when three identical coins are tossed is:
\[ \frac{7}{8} \]

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