Let

*h* = probability of getting heads in a single throw

1 -

*h* = probability of getting tails in a single throw

*h*^{2} = probability of getting 2 heads in 2 successive throws

$h^2 = 1 - h$

$h^2 + h - 1 = 0$

$h = \dfrac{-1 \pm \sqrt{1^2 - 4(1)(-1)}}{2(1)}$

$h = \dfrac{-1 \pm \sqrt{5}}{2}$

Use

$h = \dfrac{-1 + \sqrt{5}}{2}$

$h = 0.618$ ← *answer*