Parallel For Loop - Problems when adding to a List

I am having some issues involving Parallel for loops and adding to a List. The problem is, the same code may generate different output at different times. I have set up some test code below. In this code, I create a List of 10,000 int values. 1/10th of the values will be 0, 1/10th of the values will be 1, all the way up to 1/10th of the values being 9.

After setting up this List, I setup a Parallel for loop that iterates through the list. If the current number is 0, I add a value to a new List. After the Parallel for loop completes, I output the size of the list. The size should always be 1,000. Most of the time, the correct answer is given. However, I have seen 3 possible incorrect outcomes occur:

1. The size of the list is less than 1,000
2. An IndexOutOfRangeException occurs @ doubleList.Add(0.0);
3. An ArgumentException occurs @ doubleList.Add(0.0);

The message for the ArgumentException given was: Destination array was not long enough. Check destIndex and length, and the array's lower bounds.

What could be causing the errors? Is this a .Net bug? Is there something I can do to prevent this from happening?

Please try the code for yourself. If you do not get an error, try it a few times. Please also note that you probably will not see any errors using a single-core machine.

using System;
using System.Collections.Generic;
using System.Threading.Tasks;

namespace ParallelTest
{
    class Program
    {
        static void Main(string[] args)
        {
            List<int> intList = new List<int>();
            List<double> doubleList = new List<double>();

            for (int i = 0; i < 250; i++)
            {
                intList.Clear();
                doubleList.Clear();

                for (int j = 0; j < 10000; j++)
                {
                    intList.Add(j % 10);
                }

                Parallel.For(0, intList.Count, j =>
                {
                    if (intList[j] == 0)
                    {
                        doubleList.Add(0.0);
                    }
                });

                if (doubleList.Count != 1000)
                {
                    Console.WriteLine("On iteration " + i + ": List size = " + doubleList.Count);
                }
            }

            Console.WriteLine("\nPress any key to exit.");
            Console.ReadKey();
        }
    }
}