# Stacked Conditional densities

I am struggling on the following problem (altered for better understanding): Let's say the height of a father $$x_F$$ is drawn from a normal distribution $$X_{F} \sim \mathcal{N}(\mu,\sigma_F^2)$$ and the height of the son $$x_s$$ is drawn from $$X_{S} \sim \mathcal{N}(x_F,\sigma_S^2)$$, what is now the probability that both are shorter than a specific value $$h$$?

So basically $$P(X_s

My attempt: $$P(X_s

For $$P(X_s

But what about the continuous case? What would change if we start at grandpa?