Three coins are tossed once. Find the probability of getting at least one head.

Answer

To solve the problem of finding the probability of getting at least one head when three coins are tossed, we can follow these steps:

### Step 1: Determine the Sample Space
When three coins are tossed, each coin can either show heads (H) or tails (T). 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, \( n = 3 \).

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

The sample space (S) consists of the following outcomes:
- HHH
- HHT
- HTH
- HTT
- THH
- THT
- TTH
- TTT

### Step 2: Identify the Favorable Outcomes
Next, we need to find the outcomes that contain at least one head. The only outcome that does not contain a head is TTT. Therefore, the favorable outcomes for getting at least one head are:
- HHH
- HHT
- HTH
- HTT
- THH
- THT
- TTH

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

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

\[ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting the values we found:

\[ P(\text{At least one head}) = \frac{7}{8} \]

### Conclusion
Thus, the probability of getting at least one head when three coins are tossed is:

\[ \frac{7}{8} \]

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