Two coins are tossed together. Find the probability of getting :
at least one head

Answer

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

### Step 1: Determine the Sample Space
When two coins are tossed, the possible outcomes can be represented as follows:
- HH (Head on the first coin, Head on the second coin)
- HT (Head on the first coin, Tail on the second coin)
- TH (Tail on the first coin, Head on the second coin)
- TT (Tail on the first coin, Tail on the second coin)

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

### Step 2: Count the Total Number of 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 for the Event
We need to find the probability of getting at least one head. The favorable outcomes that satisfy this condition are:
- HH (2 heads)
- HT (1 head)
- TH (1 head)

Thus, the favorable outcomes (E) are:
\[ E = \{ HH, HT, TH \} \]

### Step 4: Count the Number of Favorable Outcomes
From the favorable outcomes, we can see that there are 3 outcomes that contain at least one head:
\[ \text{Favorable Outcomes} = 3 \]

### Step 5: Calculate the Probability
Using the formula for probability:
\[ P(E) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} \]
We can substitute the values we found:
\[ P(E) = \frac{3}{4} \]

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

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