Find the probability distribution for number of heads obtained in two tosses of a coin.

Explanation

To find the probability distribution for the number of heads obtained in two tosses of a coin, we can follow these steps:

### Step 1: Identify the Sample Space
When we toss a coin twice, the possible outcomes are:
- HH (Head, Head)
- HT (Head, Tail)
- TH (Tail, Head)
- TT (Tail, Tail)

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

### Step 2: Count the Total Outcomes
The total number of outcomes when tossing a coin twice is 4.

### Step 3: Define the Random Variable
Let \( X \) be the random variable representing the number of heads obtained in two tosses. The possible values of \( X \) are:
- \( X = 0 \) (no heads)
- \( X = 1 \) (one head)
- \( X = 2 \) (two heads)

### Step 4: Calculate the Probability for Each Value of \( X \)

1. **Probability of \( X = 0 \)** (0 heads):
- The only outcome with 0 heads is TT.
- Number of favorable outcomes = 1 (TT)
- Probability \( P(X = 0) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{4} \)

2. **Probability of \( X = 1 \)** (1 head):
- The outcomes with 1 head are HT and TH.
- Number of favorable outcomes = 2 (HT, TH)
- Probability \( P(X = 1) = \frac{2}{4} = \frac{1}{2} \)

3. **Probability of \( X = 2 \)** (2 heads):
- The only outcome with 2 heads is HH.
- Number of favorable outcomes = 1 (HH)
- Probability \( P(X = 2) = \frac{1}{4} \)

### Step 5: Summarize the Probability Distribution
Now we can summarize the probability distribution for the random variable \( X \):

\[ \begin{array}{|c|c|} \hline \text{Number of Heads (X)} & \text{Probability P(X)} \\ \hline 0 & \frac{1}{4} \\ 1 & \frac{1}{2} \\ 2 & \frac{1}{4} \\ \hline \end{array} \]

### Final Answer
The probability distribution for the number of heads obtained in two tosses of a coin is:
- \( P(X = 0) = \frac{1}{4} \)
- \( P(X = 1) = \frac{1}{2} \)
- \( P(X = 2) = \frac{1}{4} \)