Question

A bag contains 15 balls of the same size. Each ball is of a single colour, white, red or blue. How many red balls are there in the bag?
Statement 1: The probability of drawing a red ball is the same as that of drawing a blue ball
Statement 2: The probability of randomly drawing a white ball from the bag is 20%

• A. statement (1) alone is sufficient to answer the question
• B. statement (2) alone is sufficient to answer the question
• C. both the statements together are needed to answer the question
• D. statement (1) alone or statement (2) alone is sufficient to answer the question
• E. neither statement (1) nor statement (2) suffices to answer the question

Answer 1

The Correct Option is C

Step 1: Understand the problem.
We are given that a bag contains 15 balls of the same size, with each ball being either white, red, or blue. We are asked to find how many red balls are in the bag, based on the following statements:
- Statement 1: The probability of drawing a red ball is the same as that of drawing a blue ball.
- Statement 2: The probability of randomly drawing a white ball from the bag is 20%.

Step 2: Analyze Statement 1.
Let the number of white balls be \( w \), the number of red balls be \( r \), and the number of blue balls be \( b \). We know that the total number of balls is 15, so:
\( w + r + b = 15 \).
Statement 1 says that the probability of drawing a red ball is the same as the probability of drawing a blue ball. The probability of drawing a red ball is:
\( \frac{r}{15} \), and the probability of drawing a blue ball is:
\( \frac{b}{15} \).
Therefore, we have the equation:
\( r = b \).

Step 3: Analyze Statement 2.
Statement 2 says that the probability of drawing a white ball is 20%. The probability of drawing a white ball is:
\( \frac{w}{15} = 0.20 \).
Therefore, the number of white balls is:
\( w = 0.20 \times 15 = 3 \).

Step 4: Combine the information from both statements.
From Statement 2, we know that \( w = 3 \). Now we use the equation \( w + r + b = 15 \), which gives:
\( 3 + r + b = 15 \). Using Statement 1, \( r = b \), so we can substitute \( b \) with \( r \):
\( 3 + 2r = 15 \). Solving for \( r \):
\( 2r = 12 \)
\( r = 6 \).

Step 5: Conclusion.
The number of red balls in the bag is 6.

Final Answer:
The correct option is (C): both the statements together are needed to answer the question.