Question

o Probability Rules 10. The Committee on Student Life did a survey of 417 students regarding satisfaction with Student Government and class standing. The results follow: Freashman Sophomore Junion Total Not Satisfied Neutral Satisfied23 Total 17 61 32 3816 A3 65 80 0311A98 16 17 101 Assume the sample represents the entire population o students. Find the probability that a student selected at random is: (a) Satisfied (b) Satisfied, given the student is a Senior (c) Neutral (d) Neutral and freshman (e) Neutral, given the student is a Freshmarn (f) Senior, given satisfied (g) Are the events, Freshman and neutral independent or not? Explain SAMSUNG

Answer 1

A) P(satisfied) = 180/417 = 0.4317

B) P(satisfied | senior) = P(satisfied and senior)/P(senior)

= 65/115 = 0.5652

C) P(neutral) = 166/417 = 0.3981

D) P(neutral and freshman) = 61/417 = 0.1463

E) P(neutral | freshmen) = P(neutral and freshman)/P(fresh men) = 61/101 = 0.6040

F) P(senior | satisfied) = P(senior and satisfied)/P(satisfied)

= 65/180 = 0.3611

G) P(freshmen and neutral) = 61/417 = 0.1463

P(freshmen) * P(neutral) = 101/417 * 166/417 = 0.0964

Since P(freshmen and senior)  $\neq$ P(freshmen) * P(senior), so these two events are not independent.