In a single throw of two coins , find the probability of getting both heads or both tails .

Answer

To solve the problem of finding the probability of getting both heads or both tails when two coins are tossed, we can follow these steps:

### Step 1: Determine the Sample Space
When two coins are tossed, each coin can either land on heads (H) or tails (T). Therefore, the sample space (S) for the outcomes of tossing two coins is:
- HH (both coins show heads)
- HT (first coin shows heads, second coin shows tails)
- TH (first coin shows tails, second coin shows heads)
- TT (both coins show 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 possible outcomes when tossing two coins:
\[ \text{Total Outcomes} = 4 \]

### Step 3: Identify the Favorable Outcomes
We need to find the outcomes that are favorable to our event, which is getting either both heads or both tails. The favorable outcomes are:
- HH (both heads)
- TT (both tails)

Thus, the number of favorable outcomes is:
\[ \text{Favorable Outcomes} = 2 \]

### Step 4: Calculate the Probability
The probability (P) of an event is calculated using the formula:
\[ P(\text{Event}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]

Substituting the values we found:
\[ P(\text{Both Heads or Both Tails}) = \frac{2}{4} = \frac{1}{2} \]

### Final Answer
The probability of getting both heads or both tails when two coins are tossed is:
\[ \frac{1}{2} \]

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