Problem 3 [10 points = 4 + 3 + 3] Students on campus are interviewed about their dream careers. The most popular school choices were Business (event B) and Law (event _). . The historic data show that 75% of respondents are not willing to pursue career in Law, so P [L'] = 0.75 . It also is known that 40% of students would like to join School of Business, so P [B] = 0.40 . In addition, proportion of those who are not interested in either Law or Business Schools was 35%, so that P[B' L'] = 0.35 1. Fill all joint and marginal probabilities in the table below. 2. Are two events, B and L, independent? Justify your answer! 3. Evaluate the relative (conditional) proportion of respondents who are not pursuing careers in Law, among those who are heading to Business. Find P [L'|B] B occurs B does not occur Marginal L occurs L does not occur P [B'nL'] = 0.35 P[L'] = 0.75 Marginal P [L] = 0.40 Solution