Each of the following question is followed by three statements I, II and III. You have to study the question and the statements and decide which of the statements is/are necessary to answer the question.
What is the probability of drawing a red ball from a bag containing red, blue and green balls?
I. There are total 20 balls in the bag.
II. The ratio of red, blue and green balls is 5:3:2.
III. There are 10 red balls in the bag.

Options

A. Only Statement li is sufficient.
B. Only Statements I and II together are sufficient.
C. Only Statements II and III together are sufficient.
D. Any two of the three statements together.

Answer

To determine the probability of drawing a red ball from a bag containing red, blue, and green balls, we need to analyze the provided statements.

**Step 1: Understand the question**
The question asks for the probability of drawing a red ball from a bag that contains red, blue, and green balls. The probability can be calculated using the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

**Step 2: Analyze Statement I**
Statement I states that there are a total of 20 balls in the bag. This gives us the total number of balls, but we still need to know how many of those are red to calculate the probability.

**Step 3: Analyze Statement II**
Statement II provides the ratio of red, blue, and green balls as 5:3:2. This information is useful because it allows us to find the number of red balls if we know the total number of balls.

**Step 4: Analyze Statement III**
Statement III states that there are 10 red balls in the bag. This directly provides the number of red balls, which is necessary to calculate the probability.

**Step 5: Combine the statements**
- If we use Statement I (total of 20 balls) and Statement II (ratio of 5:3:2), we can find the number of red balls. The ratio indicates that the total parts are \(5 + 3 + 2 = 10\). Thus, each part equals \(20 \div 10 = 2\). Therefore, the number of red balls is \(5 \times 2 = 10\).
- If we use Statement I (total of 20 balls) and Statement III (10 red balls), we can directly calculate the probability as:
\[ \text{Probability} = \frac{10}{20} = \frac{1}{2} \]
- If we use Statement II (ratio of red, blue, green) and Statement III (10 red balls), we can also confirm the total number of balls as 20 and calculate the probability.

**Step 6: Conclusion**
To find the probability of drawing a red ball, we can conclude that:
- Any two of the three statements are sufficient to answer the question. Thus, the answer is that we need any two of the three statements to determine the probability.

**Final Answer:**
The answer is D: Any two of the three statements are sufficient to answer the question.

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