MVC4: Two radio buttons for a single boolean model property

I'm attempting to find the correct Razor syntax for mutually exclusive radio buttons that both reflect the value of a boolean property on my model. My model has this:

public bool IsFemale{ get; set; }

I would like to display this with two radio buttons, one "Male" and the other "Female," but everything I've tried so far has not reflected the actual value of the IsFemale property on the model. Currently, I have this:

@Html.RadioButtonFor(model => model.IsFemale, !Model.IsFemale) Male
@Html.RadioButtonFor(model => model.IsFemale, Model.IsFemale) Female

This seems to persist the value correctly if I change and update, but does not mark the correct value as checked. I'm sure this is something stupid, but I'm stuck.

Try like this:

@Html.RadioButtonFor(model => model.IsFemale, "false") Male
@Html.RadioButtonFor(model => model.IsFemale, "true") Female

And here's the full code:

Model:

public class MyViewModel
{
    public bool IsFemale { get; set; }
}

Controller:

public class HomeController : Controller
{
    public ActionResult Index()
    {
        return View(new MyViewModel
        {
            IsFemale = true
        });
    }

    [HttpPost]
    public ActionResult Index(MyViewModel model)
    {
        return Content("IsFemale: " + model.IsFemale);
    }
}

View:

@model MyViewModel

@using (Html.BeginForm())
{
    @Html.RadioButtonFor(model => model.IsFemale, "false", new { id = "male" }) 
    @Html.Label("male", "Male")

    @Html.RadioButtonFor(model => model.IsFemale, "true", new { id = "female" })
    @Html.Label("female", "Female")
    <button type="submit">OK</button>
}

In MVC 6 (ASP.NET Core) this can also be achieved with tag helpers:

<label>
    <input type="radio" asp-for="IsFemale" value="false" /> Male
</label>
<label>
    <input type="radio" asp-for="IsFemale" value="true" /> Female
</label>