marcia and john are playing the following game: marcia thinks of a fraction, and john flips a coin. if the coin turns up heads, marcia multiplies the number she's thinking of by $\frac{7}{8}$. if the coin turns up tails, she multiplies the number she's thinking of by $\frac{8}{7}$. john flips the coin ten times, and after each flip marcia multiplies the number in her head by either $\frac{7}{8}$ or $\frac{8}{7}$, depending on the coin flip. the ten coin flips turn out to be:\[ \text{h that h}, \]where h means 'heads' and t means 'tails.' what number is marcia thinking of at the end of the game if she starts out with the fraction $\frac{1}{3}$?