Ram and Priya are playing a game. Ram's winning probability is `1/3` and sum of their winning probabilities is 1. Numerator of Priya's winning probability is ______

Options

A. 0
B. 1
C. `1//3`
D. None of these

Answer

To solve the problem step by step, we will find the numerator of Priya's winning probability based on the information given.

### Step 1: Understand the winning probabilities
We know that:
- Ram's winning probability (P(Ram)) = 1/3
- The sum of their winning probabilities is 1.

### Step 2: Set up the equation
Let Priya's winning probability be P(Priya). According to the problem:
\[ P(Ram) + P(Priya) = 1 \]

### Step 3: Substitute Ram's probability into the equation
We can substitute the value of Ram's winning probability into the equation:
\[ \frac{1}{3} + P(Priya) = 1 \]

### Step 4: Solve for Priya's winning probability
To find P(Priya), we can rearrange the equation:
\[ P(Priya) = 1 - \frac{1}{3} \]

### Step 5: Calculate the value
Now, we calculate:
\[ P(Priya) = \frac{3}{3} - \frac{1}{3} = \frac{2}{3} \]

### Step 6: Identify the numerator
The winning probability of Priya is \( \frac{2}{3} \). The numerator of Priya's winning probability is therefore 2.

### Final Answer
The numerator of Priya's winning probability is **2**.

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