 Because of studying’s effect on the probability of passing, \(P(P\mid S) \gt P(P\mid {\sim}S)\) and \(P({\sim}P\mid S) \lt P({\sim}P\mid {\sim}S)\). So \(\textit{EU} (S) \gt \textit{EU} ({\sim}S)\), assuming that studying’s increase in the probability of passing compensates for the effort of studying. Maximization of expected utility recommends studying.