Each of the following question is followed by two statements I, and Il. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
What is the probability of drawing 2 red balls?
Statement I: there are 4 red and 5 blue balls in the bag.
Statement II: there are 20 balls in the bag out of which 5 are yellow and rest are blue & red.

Options

A. Only Statement I alone.
B. Only Statement II alone.
C. Both Statements I and II together.
D. Neither Statement I nor II is sufficient

Answer

To determine the probability of drawing 2 red balls from a bag, we need to analyze the provided statements.

### Step-by-Step Solution:

1. **Understanding the Question**: We need to find the probability of drawing 2 red balls from a bag. The probability formula is:
\[ P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} \]

2. **Analyzing Statement I**:
- Statement I states that there are 4 red and 5 blue balls in the bag.
- This means the total number of balls in the bag is:
\[ \text{Total balls} = 4 \text{ (red)} + 5 \text{ (blue)} = 9 \text{ balls} \]
- The number of favorable outcomes for drawing 2 red balls can be calculated using combinations:
\[ \text{Favorable outcomes} = \binom{4}{2} = \frac{4 \times 3}{2 \times 1} = 6 \]
- The total outcomes for drawing 2 balls from 9 is:
\[ \text{Total outcomes} = \binom{9}{2} = \frac{9 \times 8}{2 \times 1} = 36 \]
- Therefore, the probability of drawing 2 red balls is:
\[ P(\text{2 red}) = \frac{6}{36} = \frac{1}{6} \]
- **Conclusion**: Statement I is sufficient to answer the question.

3. **Analyzing Statement II**:
- Statement II states that there are 20 balls in the bag, out of which 5 are yellow, and the rest are blue and red.
- This means there are 15 balls that are either red or blue, but it does not specify how many are red and how many are blue.
- Without knowing the exact number of red balls, we cannot determine the probability of drawing 2 red balls.
- **Conclusion**: Statement II is not sufficient to answer the question.

### Final Conclusion:
- Only Statement I is sufficient to answer the question about the probability of drawing 2 red balls.
- Therefore, the answer is **Option 1**: Only Statement I alone is sufficient.