Two coins are tossed simultaneously. The probability of getting at most one head is

Options

A. `(1)/(4)`
B. `(1)/(2)`
C. `(2)/(3)`
D. `(3)/(4) `

Answer

To find the probability of getting at most one head when two coins are tossed, we can follow these steps:

### Step 1: Identify the Sample Space
When we toss two coins, the possible outcomes (sample space) are:
1. HH (both heads)
2. HT (first head, second tail)
3. TH (first tail, second head)
4. TT (both tails)

Thus, the sample space 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: Define the Event of Interest
We need to find the probability of getting at most one head. This means we want to count the outcomes that have either 0 heads or 1 head.

### Step 4: Identify Favorable Outcomes
The outcomes that satisfy the condition of having at most one head are:
1. HT (1 head)
2. TH (1 head)
3. TT (0 heads)

Thus, the favorable outcomes are:
\[ F = \{ HT, TH, TT \} \]

### Step 5: Count the Favorable Outcomes
From the favorable outcomes, we can see that there are 3 outcomes.

### Step 6: Calculate the Probability
The probability \( P \) of getting at most one head is given by the formula:
\[ P(\text{at most one head}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{4} \]

### Final Answer
Thus, the probability of getting at most one head when two coins are tossed is:
\[ \frac{3}{4} \]

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