A coin is tossed twice, then find the probability that a head is obtained atleast once.

Answer

To solve the problem of finding the probability of obtaining at least one head when a coin is tossed twice, we can follow these steps:

### Step 1: Determine the Sample Space
When a coin is tossed twice, the possible outcomes can be listed as follows:
- HH (Head, Head)
- HT (Head, Tail)
- TH (Tail, Head)
- TT (Tail, Tail)

So, 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 possible outcomes when a coin is tossed twice.

### Step 3: Identify the Favorable Outcomes
Next, we need to identify the outcomes that contain at least one head. The favorable outcomes are:
- HH (Head, Head)
- HT (Head, Tail)
- TH (Tail, Head)

So, the favorable outcomes are:
\[ F = \{ HH, HT, TH \} \]

### Step 4: Count the Favorable Outcomes
From the favorable outcomes, we can see that there are 3 outcomes that contain at least one head.

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

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

### Final Answer
Thus, the probability of obtaining at least one head when a coin is tossed twice is:
\[ \frac{3}{4} \]

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