Dropping multiple objects using an array in Actionscript?

They might not be dropping as often as you want to because you're only removing one per enter frame event using this code:

if (fireBalls.length>0&&fireBalls[0].y>stage.stageHeight){ // Fireballs exit stage
    removeChild(fireBalls[0]);
    fireBalls.shift();
}

You might want to use a for loop instead to go through all of the fireballs on every enter frame event like so:

for (var i:int = 0; i < fireBalls.length; ++i)
{
    if (fireBalls.length > 0 && fireBalls[i].y > stage.stageHeight)
    {
        removeChild(fireballs[i]);
    }
}

As far as I can tell, your usage of Math.random() is correct, if you want a new fireball about 1/5th of the time.

figured it out

import flash.events.TimerEvent;
import flash.utils.Timer;
var bucket:Bucket=new Bucket
var sun:Sun=new Sun
var fireBalls:Array=new Array()
var livesLeft:Array = new Array()
var left:Boolean;
var timer:Timer = new Timer(1000); // test change direction every second

addChild(bucket)
addChild(sun)
sun.x=sun.width/2
sun.y=50
bucket.x=bucket.width/2
bucket.y=stage.stageHeight-50
bucket.speed=15

stage.addEventListener(KeyboardEvent.KEY_DOWN, onKeyDown)

function onTimer(e:TimerEvent) {
    left = (Math.random() > 0.75);// 50/50 chance of changing direction
}
timer.addEventListener(TimerEvent.TIMER, onTimer);
timer.start();

function onKeyDown(event:KeyboardEvent){
    if (event.keyCode==37&&bucket.x>bucket.width/2){ // left arrow key
        bucket.x=bucket.x-bucket.speed;
    }
    if (event.keyCode==39&&bucket.x<stage.stageWidth-bucket.width/2){ // right arrow key
        bucket.x=bucket.x+bucket.speed;
    }
}

stage.addEventListener(MouseEvent.MOUSE_MOVE,followBucket);

function followBucket(event:MouseEvent):void {
bucket.x=mouseX;
}

addEventListener(Event.ENTER_FRAME,onEnterFrame)

function checkForCollisions (){

}

function onEnterFrame(event:Event){
    checkForCollisions.call();
    if (left) {
        sun.x = sun.x - 15;
    }else{
        sun.x = sun.x + 15;
    }
    if (fireBalls.length>0&&fireBalls[0].y>stage.stageHeight){ // Fireballs exit stage
        removeChild(fireBalls[0]);
        fireBalls.shift();
    }
    for (var j:int=0; j<fireBalls.length; j++){
        fireBalls[j].y=fireBalls[j].y+15;
    }   
    if (Math.random()<.2){ // Fireballs shooting from Sun
        var fireBall:FireBall=new FireBall;
        fireBall.x=sun.x;
        fireBall.y=sun.y+sun.width/2;
        addChild(fireBall);
        fireBall.gotoAndStop(1);
        fireBalls.push(fireBall);
    }
    if (sun.x>stage.stageWidth){ // Sun hits right side of stage
        sun.x=0;
    }
    if (sun.x<0){ // Sun hits left side of stage
        sun.x=stage.stageWidth;
    }
}