using Bayes’ Rule to calculate conditional probability i have following problem,
"Students who party before an exam are twice as likely to fail the exam as those who don't party (and presumably study). Of 20% of students partied before the exam, what percentage of students who failed the exam went partying?"
i believe that this problem related to conditional probability, but i couldn't find all necessary elements for answer. appreciate your help.

Let $x$ be the total number of students and $p$ be the probability of a student who didn't party failing the exam. The probability of a student who partied before the exam failing the exam is then $2p$.
$x/5$ students partied, out of which $2px/5$ failed. Out of the $4x/5$ who didn't party, $4px/5$ failed the exam. The total students who failed is $2px/5+4px/5=6px/5$, out of which $2px/5$ partied. The required probability is $2/6=1/3$.
