Pick a random content area item:

public virtual ContentArea ContentArea { get; set; }

public ContentAreaItem RandomItem
{
    get
    {
        var random = new Random();
        return ContentArea?.FilteredItems.OrderBy(x => random.Next()).FirstOrDefault();
    }
}

An alternative approach would be to make a Random Visitor Group and then personalising the blocks in the content area.  

var random = new Random(unchecked((int)(DateTime.Now.Ticks)));
IList<ContentAreaItem> randomItemsList = contentAreaItemsList.OrderBy(t => random.Next(contentAreaItemsList.Count)).ToList();

I thought you wanted to pick one content area item randomly.

Your own answer, that you accepted as the answer, returns all items in random order.