2010 AMC 12A Question 15 - thichhoctoan.com

Question 15

A coin is altered so that the probability that it lands on heads is less than $\dfrac12,$ and when the coin is flipped four times, the probability of an equal number of heads and tails is $\dfrac{1}{6}.$ What is the probability that the coin lands on heads?

$\dfrac{\sqrt{15}-3}{6}$
$\dfrac{6-\sqrt{6\sqrt6+2}}{12}$
$\dfrac{\sqrt2-1}{2}$
$\dfrac{3-\sqrt3}{6}$
$\dfrac{\sqrt3-1}{2}$