Bayes for heavy preparers among offer holders

Among students, $25\%$ prepare heavily on a study platform, $30\%$ prepare lightly and $45\%$ do not use it. A heavy user is twice as likely to land an offer as a light user, and a light user is twice as likely as a non-user. Given that a student has an offer, what is the probability that they were a heavy user?

$\tfrac{20}{41}$. Let non-users succeed with probability $p$, so light users have $2p$ and heavy users $4p$. By Bayes, the posterior is $\tfrac{0.25\cdot4p}{0.25\cdot4p+0.3\cdot2p+0.45\cdot p}=\tfrac{1}{2.05}=\tfrac{20}{41}$; the unknown $p$ cancels.