Find the probability of getting at least one head in three throws of a coin.

Explanation

To find the probability of getting at least one head in three throws of a coin, we can follow these steps:

### Step 1: Determine the total number of outcomes
When we throw a coin three times, each throw has 2 possible outcomes: heads (H) or tails (T). Therefore, the total number of outcomes for three throws is calculated as follows:

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

### Step 2: Identify the outcome with no heads
The only outcome where there are no heads at all in three throws is when all three throws result in tails. This outcome can be represented as:

\[ \text{Outcome with no heads} = TTT \]

Thus, there is only 1 way to get no heads.

### Step 3: Calculate the probability of getting no heads
The probability of getting no heads (i.e., all tails) can be calculated by dividing the number of favorable outcomes (which is 1) by the total number of outcomes (which is 8):

\[ P(\text{No heads}) = \frac{\text{Number of outcomes with no heads}}{\text{Total outcomes}} = \frac{1}{8} \]

### Step 4: Calculate the probability of getting at least one head
To find the probability of getting at least one head, we can use the complement rule. The complement of getting at least one head is getting no heads. Therefore, we can express the probability of getting at least one head as:

\[ P(\text{At least one head}) = 1 - P(\text{No heads}) \]

Substituting the value we found in Step 3:

\[ P(\text{At least one head}) = 1 - \frac{1}{8} = \frac{7}{8} \]

### Final Answer
The probability of getting at least one head in three throws of a coin is:

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

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