Option B: is double the number of green balls.
Let's break down the problem step by step:
     ● Statement 1: There are as many red balls as there are yellow balls.  
           ○ Let the number of red balls be \( R \).
           ○ Let the number of yellow balls be \( Y \).
           ○ According to the statement, \( R = Y \).
     ● Statement 2: There are twice as many yellow balls as there are green ones.  
           ○ Let the number of green balls be \( G \).
           ○ According to the statement, \( Y = 2G \).
     ● Statement 3: We need to determine the relationship between the number of red balls and the other balls.  
     Now, let's analyze the options:
     ● Option A: The number of red balls is equal to the sum of yellow and green balls.  
           ○ This implies \( R = Y + G \).
           ○ Substituting \( R = Y \) and \( Y = 2G \), we get \( Y = 2G \) and \( G = G \).
           ○ Therefore, \( R = 2G + G = 3G \), which contradicts \( R = Y = 2G \).
           ○ Hence, Option A is incorrect.
     ● Option B: The number of red balls is double the number of green balls.  
           ○ This implies \( R = 2G \).
           ○ Since \( R = Y \) and \( Y = 2G \), we have \( R = 2G \).
           ○ This matches the condition given in the problem.
           ○ Hence, Option B is correct.
     ● Option C: The number of red balls is equal to yellow balls minus green balls.  
           ○ This implies \( R = Y - G \).
           ○ Substituting \( R = Y \) and \( Y = 2G \), we get \( R = 2G - G = G \).
           ○ This contradicts \( R = Y = 2G \).
           ○ Hence, Option C is incorrect.
     ● Option D: The number of red balls cannot be ascertained.  
           ○ We have already determined that \( R = 2G \).
           ○ Hence, Option D is incorrect.
     Therefore, the correct answer is Option B: The number of red balls is double the number of green balls.