Gien that X is discrete random variable which take the values, `0,1,2 and P(X=0)=(144)/(169),P(X=1)=(1)/(169)`, then the value of `P(X=2)` is

Options

A. `(145)/(169)`
B. `(24)/(169)`
C. `(2)/(169)`
D. `(143)/(169)`

Explanation

To find the value of \( P(X=2) \) given the probabilities for \( P(X=0) \) and \( P(X=1) \), we can use the property that the sum of the probabilities for all possible outcomes of a discrete random variable must equal 1.

### Step-by-Step Solution:

1. **Identify the given probabilities**:
- \( P(X=0) = \frac{144}{169} \)
- \( P(X=1) = \frac{1}{169} \)
- Let \( P(X=2) = p \).

2. **Set up the equation**:
According to the property of probabilities:
\[ P(X=0) + P(X=1) + P(X=2) = 1 \]
Substituting the known values:
\[ \frac{144}{169} + \frac{1}{169} + p = 1 \]

3. **Combine the fractions**:
Combine \( P(X=0) \) and \( P(X=1) \):
\[ \frac{144 + 1}{169} + p = 1 \]
This simplifies to:
\[ \frac{145}{169} + p = 1 \]

4. **Isolate \( p \)**:
To find \( p \), subtract \( \frac{145}{169} \) from both sides:
\[ p = 1 - \frac{145}{169} \]

5. **Convert 1 to a fraction**:
Convert 1 into a fraction with a denominator of 169:
\[ 1 = \frac{169}{169} \]
So the equation becomes:
\[ p = \frac{169}{169} - \frac{145}{169} \]

6. **Perform the subtraction**:
\[ p = \frac{169 - 145}{169} = \frac{24}{169} \]

7. **Conclusion**:
Therefore, the value of \( P(X=2) \) is:
\[ P(X=2) = \frac{24}{169} \]