This is about game theory in economics. Please show all your workings step by step and answers too.

Return to the internship game from Lecture 8. Suppose a student's beliefs as to What the other 9 students will do are as follows: with a probability of 0.2, three of them will apply to JPM and six of them to LM; With a probability of 0.5, four of them will apply to JPM and five of them to LM; and with a probability of 0.3, ve of them will apply to JPM and four of them to LM. Assume a student Chooses so as to maximize his expected utility, where will he apply