An event 'E' is defined as getting both heads or both tails in a throw of two coins, then find P(E) …………….

Answer

To find the probability of the event 'E', which is defined as getting both heads or both tails in a throw of two coins, we can follow these steps:

### Step 1: Define the Sample Space
When we throw two coins, the possible outcomes can be represented as:
- HH (both heads)
- HT (first head, second tail)
- TH (first tail, second head)
- TT (both tails)

Thus, the sample space \( S \) consists of these outcomes:
\[ S = \{ HH, HT, TH, TT \} \]

### Step 2: Count the Total Number of Outcomes
The total number of outcomes in the sample space \( S \) is:
\[ n(S) = 4 \]

### Step 3: Define the Event 'E'
The event 'E' is defined as getting both heads (HH) or both tails (TT). Therefore, we can list the outcomes that satisfy this event:
- HH (both heads)
- TT (both tails)

### Step 4: Count the Favorable Outcomes
Now, we need to count the number of favorable outcomes for event 'E':
- The favorable outcomes are: HH and TT.
Thus, the number of favorable outcomes \( n(E) \) is:
\[ n(E) = 2 \]

### Step 5: Calculate the Probability of Event 'E'
The probability \( P(E) \) of event 'E' can be calculated using the formula:
\[ P(E) = \frac{n(E)}{n(S)} \]
Substituting the values we found:
\[ P(E) = \frac{2}{4} = \frac{1}{2} \]

### Final Answer
Thus, the probability of getting both heads or both tails in a throw of two coins is:
\[ P(E) = \frac{1}{2} \]

---