1. if (ballX > WIDTH - PAD_WIDTH ) {
       if (ballY > PAD_Y && ballY < PAD_Y + PAD_HEIGHT) {
         // bounce
       }
       else {
         // game over
       }
     }
   

But to make things more accurat, you should maybe calculate where the ball would be on the next frame. Then test, if it hit any obstacle, then adjust the position of the ball if it bounces.

• if balls y-value >= y-paddle (upper bound of the paddle) and
• balls y-value <= y-paddle+ PAD_HEIGHT (lower bound of the paddle)

• mouse steers paddle
• you can start over now
• note line 63, not needed
  

1. final int WIDTH = 400, HEIGHT = WIDTH;
2. final color WHITE = color(255);
3. final color BLACK = color(0);
4. final color RED = color(255, 0, 0);
5. final color GREEN = color(0, 255, 0);
6. final color BLUE = color(0, 0, 255); 
7. // Ball constants
8. final int RAD= 5;
9. final int MAX_SPEED= 5;
10. //Pad constants
11. final int PAD_WIDTH= 5;
12. final int PAD_HEIGHT= 40;
13. final int PAD_X= WIDTH - PAD_WIDTH * 2;
14. final int PAD_SPEED= 20;
15. //Distance between walls and the ball
16. // LW= left wall distance, RW= right wall distance
17. // TW= top wall distance, BW= bottom wall distance
18. final int LW=RAD, RW = WIDTH - RAD, TW=RAD, BW= HEIGHT- RAD;
19. //global game variables
20. int ballX, ballY, speedX, speedY, PAD_Y, points;
21. void setup()
22. {
23.   size(WIDTH, HEIGHT);
24.   startUp();
25. }
26. void startUp() {
27.   ellipseMode(RADIUS);
28.   ballX= WIDTH/2;
29.   ballY= HEIGHT/2;
30.   speedX= -int(random(3, MAX_SPEED));
31.   speedY= int(random(3, MAX_SPEED));
32.   PAD_Y=(HEIGHT- PAD_HEIGHT) / 2;  
33.   points= 0;
34. }
35. void draw()
36. {
37.   background(WHITE);
38.   noStroke();
39.   smooth();
40.   fill(RED);
41.   ellipse(ballX, ballY, RAD, RAD);
42.   fill(BLUE);
43.   PAD_Y = mouseY;
44.   rect(PAD_X, PAD_Y, PAD_WIDTH, PAD_HEIGHT);
45.   ballX= ballX + speedX;
46.   ballY= ballY + speedY;
47.   //If the ball hits the LW, TW, or BW, it will bounce back.
48.   if (ballX < LW) {
49.     speedX = -speedX;
50.   }
51.   if (ballY < TW || ballY > BW) {
52.     speedY = -speedY;
53.   }
54.   if (ballX > WIDTH || ballY > WIDTH) {
55.     println("GAME OVER");
56.     startUp();
57.     //exit();
58.   }
59.   //THIS IS WHERE I'M CONFUSED
60.   if (ballX >= PAD_X-5 &&
61.     ballY >= PAD_Y && ballY <= PAD_Y + PAD_HEIGHT) {
62.     speedX=-abs(speedX); 
63.     //speedY=-speedY; 
64.     points= points + 1;
65.     println(points);
66.   }
67. }
68. //THIS IS WHERE I'M CONFUSED
69. void keyPressed()
70. {
71.   if (key == CODED) {
72.     if (keyCode == UP) {
73.       if (PAD_Y >= PAD_SPEED) {
74.         PAD_Y -= PAD_SPEED;
75.       }
76.     }
77.     else if (keyCode == DOWN) {
78.       if (PAD_Y <= HEIGHT - PAD_HEIGHT - PAD_SPEED)
79.       {
80.         PAD_Y += PAD_SPEED;
81.       }
82.     }
83.   }
84. }