A pair of coins is tossed once. Then the probability of showing at lest one head is ___________.

Answer

To solve the problem of finding the probability of showing at least one head when a pair of coins is tossed once, we can follow these steps:

### Step 1: Identify the Sample Space
When tossing two coins, the possible outcomes can be listed as follows:
- HH (both coins show heads)
- HT (first coin shows heads, second coin shows tails)
- TH (first coin shows tails, second coin shows heads)
- TT (both coins show tails)

Thus, the sample space \( S \) is:
\[ S = \{ HH, HT, TH, TT \} \]

### Step 2: Count the Total Outcomes
From the sample space, we can see that there are a total of 4 outcomes.

### Step 3: Identify Favorable Outcomes
Next, we need to determine the outcomes that show at least one head. The favorable outcomes from our sample space are:
- HH (two heads)
- HT (one head, one tail)
- TH (one head, one tail)

The only outcome that does not show at least one head is:
- TT (two tails)

Thus, the favorable outcomes are:
\[ \{ HH, HT, TH \} \]

### Step 4: Count the Favorable Outcomes
The number of favorable outcomes is 3 (HH, HT, TH).

### Step 5: Calculate the Probability
The probability \( P \) of an event is given by the formula:
\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting the values we found:
\[ P(\text{at least one head}) = \frac{3}{4} \]

### Final Answer
The probability of showing at least one head when a pair of coins is tossed once is:
\[ \frac{3}{4} \]

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