Answer
The largest frequency of heterozygous carriers occurs when $p=0.5$.
Work Step by Step
The frequency of heterozygous carriers is $y=2p(1-p)$, which is an inverted parabola $(\cap-\text{shaped})$ curve.
The curve is symmetric about the vertical line passing through the maximum point.
The y-coordinate is $0$ when $2p(1-p)=0$, or, $p(1-p)=0$, which gives $p=0$ and $p=1$, which are the roots.
The line of symmetry passes from the mid of the roots, i.e., $p=0.5$ is the line of symmetry. Now, the maximum point lies on the line of symmetry, so, the largest frequency of heterozygous carriers occurs when $p=0.5$.
