Two unbiassed coins are tossed. Find the proability of getting at the most one head.

Answer

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

### Step 1: Identify the Sample Space
When two coins are tossed, the possible outcomes can be listed as follows:
1. Head (H), Head (H) - HH
2. Head (H), Tail (T) - HT
3. Tail (T), Head (H) - TH
4. Tail (T), Tail (T) - TT

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

### Step 2: Count the Total Outcomes
The total number of outcomes when tossing two coins is:
\[ \text{Total outcomes} = 4 \]

### Step 3: Define Favorable Outcomes
We need to find the outcomes that result in "at most one head." This means we can have either:
- No heads (0 heads)
- One head (1 head)

From the sample space, we can identify the favorable outcomes:
1. No heads: TT
2. One head: HT, TH

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

### Step 4: Count the Favorable Outcomes
The number of favorable outcomes is:
\[ \text{Favorable outcomes} = 3 \]

### Step 5: Calculate the Probability
The probability (P) of getting at most one head is given by the formula:
\[ P(\text{at most one head}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} \]

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

### Final Answer
The probability of getting at most one head when tossing two unbiased coins is:
\[ \frac{3}{4} \]

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