Answer
See below.
Work Step by Step
Let $P(H)=x$, then $P(T)=2x$. We also know that $P(T)+P(H)=1$, thus $2x+x=1\\3x=1\\x=\frac{1}{3}$.
Thus $P(T)=\frac{2}{3},P(H)=\frac{1}{3}$.
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