The correct answer is option (C):
both the statements together are needed to answer the question
Let's analyze the problem and each statement to determine the number of red balls in the bag.
Statement 1: The probability of drawing a red ball is the same as that of drawing a blue ball.
This tells us that the number of red balls is equal to the number of blue balls. Let 'r' be the number of red balls, 'b' be the number of blue balls, and 'w' be the number of white balls. From this statement, we know r = b. We also know that r + b + w = 15. However, we can't determine the exact value of 'r' (the number of red balls) with this information alone because we don't know the value of 'w'.
Statement 2: The probability of randomly drawing a white ball from the bag is 20%.
This means that the number of white balls, 'w', is 20% of the total number of balls (15). Therefore, w = 0.20 * 15 = 3. However, this statement doesn't tell us anything about the relationship between red and blue balls. We still don't know the number of red balls.
Combining the statements:
From Statement 1, we know r = b.
From Statement 2, we know w = 3.
Also, we know that r + b + w = 15.
Substituting the value of 'w', we get r + b + 3 = 15.
Simplifying this equation, we get r + b = 12.
Since r = b, we can substitute 'r' for 'b', giving us r + r = 12.
This simplifies to 2r = 12.
Therefore, r = 6.
By combining both statements, we were able to determine the number of red balls. Thus, both statements are required to answer the question.