two fair coins are tossed simultaneously . Find the probability of
getting atleast one head .

Options

A. `1/4`
B. `3/4`
C. `1/2`
D. `3/8`

Answer

To solve the problem of finding the probability of getting at least one head when two fair coins are tossed simultaneously, we will follow these steps:

### Step 1: Identify the Sample Space
When two coins are tossed, the possible outcomes can be listed as follows:
1. HH (both coins show heads)
2. HT (first coin shows heads, second coin shows tails)
3. TH (first coin shows tails, second coin shows heads)
4. 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:
\[ \text{Total outcomes} = 4 \]

### Step 3: Identify the Favorable Outcomes
Next, we need to find the outcomes that satisfy the condition of getting at least one head. The favorable outcomes are:
1. HH (both heads)
2. HT (first head, second tail)
3. TH (first tail, second head)

The only outcome that does not satisfy the condition is:
- TT (both tails)

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

### Step 4: Count the Favorable Outcomes
From the favorable outcomes, we can see that there are 3 outcomes that meet the condition:
\[ \text{Favorable outcomes} = 3 \]

### Step 5: Calculate the Probability
The probability \( P \) of getting at least one head can be calculated using the formula:
\[ P(\text{at least one head}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{4} \]

### Final Answer
The probability of getting at least one head when two fair coins are tossed is:
\[ \frac{3}{4} \]

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