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The problem in the image reads as follows:

**Problem:**
An urn contains 9 red, 7 white, and 4 black balls. What is the probability that a randomly chosen ball is not red? If \( x \) black balls are added, the probability of drawing a black ball becomes 4 times what it was originally. Find \( x \).

### Step-by-Step Solution:

1. **Total Balls in the Urn (initially):**
   The urn contains 9 red, 7 white, and 4 black balls.
   \[
   \text{Total balls} = 9 + 7 + 4 = 20
   \]

2. **Probability that a ball is not red:**
   The number of non-red balls (white + black) is:
   \[
   7 + 4 = 11
   \]
   Therefore, the probability that the ball is not red is:
   \[
   P(\text{not red}) = \frac{11}{20}
   \]

3. **Probability of drawing a black ball (initially):**
   The probability of drawing a black ball before adding any additional black balls is:
   \[
   P(\text{black initially}) = \frac{4}{20} = \frac{1}{5}
   \]

4. **After adding \( x \) black balls:**
   The total number of balls becomes \( 20 + x \), and the total number of black balls becomes \( 4 + x \).
   The new probability of drawing a black ball is:
   \[
   P(\text{black after}) = \frac{4 + x}{20 + x}
   \]

5. **The new probability is 4 times the original:**
   We are told that after adding \( x \) black balls, the probability of drawing a black ball is 4 times the original probability. Therefore, we set up the following equation:
   \[
   \frac{4 + x}{20 + x} = 4 \times \frac{1}{5} = \frac{4}{5}
   \]

6. **Solve the equation:**
   To solve for \( x \), cross-multiply:
   \[
   5(4 + x) = 4(20 + x)
   \]
   Expanding both sides:
   \[
   20 + 5x = 80 + 4x
   \]
   Rearrange the equation:
   \[
   5x - 4x = 80 - 20
   \]
   Simplify:
   \[
   x = 60
   \]

Therefore, \( x = 60 \).

### Final Answer:
The number of black balls added is \( \boxed{60} \).

---

Would you like more details on any part of this solution, or have any other questions?

Here are 5 related questions you could explore:
1. What is the new total number of balls after adding 60 black balls?
2. What is the new probability of drawing a non-red ball after the addition of black balls?
3. If instead of black, 60 white balls were added, how would the probability change?
4. How would the probability of drawing a red ball change after the addition of 60 black balls?
5. What would be the probability of drawing any ball (red, white, or black) if \(x\) was negative (removing balls)?

**Tip:** When dealing with probabilities that change due to added or removed items, always adjust both the favorable outcomes and the total outcomes carefully to set up the correct equation.

An urn contains 9 red, 7 white, and 4 black balls. What is the probability that it is not red? If x black balls are added, then the probability of drawing a black ball is 4 times what it was earlier. Find x.

Explore this probability problem involving an urn containing 9 red, 7 white, and 4 black balls. Learn how to find the probability that a randomly chosen ball is not red and how to determine the number of black balls to add to make the probability of drawing a black ball four times its original value. Suitable for students in Grades 9-12.

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