Two psychologists surveyed 478 children in grades 4, 5, and 6 in elementary schools in Michigan. They stratified their sample, drawing roughly 1/3 from rural, 1/3 from suburban, and 1/3 from urban schools. Among other questions, they asked the students whether their primary goal was to get good grades, to be popular, or to be good at sports. Below is a contingency table giving counts of the students by their goals and sex. Goals Sex Grades Popular Sports Boy 117 50 60 Girl 130 91 30

(a) If we select a student at random from this study, what is the probability that we will select a boy? (b) What is the probability that we select a student whose goal is to be good at sports? (c) What is the probability that we will select a student that is a boy and whose goal is to be good at sports? (d) What is the probability that we will select a boy or a student whose goal is to be good at sports? (e) What is the probability that a selected student wants to be good at sports given that we have selected a boy? (f) Are the variables Sex and Goals independent? You must use a valid probability formula to support your answer.