Question

A corporation only recruits applications who attended one of three schools: College A, B and C. The director HR knows that 10% of the job applicants attended A, 30% attended B and the rest attended C. However 60% of all applicants from A, are offered positions in the Corporation, whereas only 35% of applicants from B and 25% of applicants from C are given offers.

i) What percentage of offer letters go to applicants from College A?

ii) What percentage of offer letters go to applicants from College B?

iii) What percentage of offer letters go to applicants from College C?

Answer 1

P(college A) = 0.1

P(college B) = 0.3

P(college C) = 1 - (0.1 + 0.3) = 0.6

P(offered position | college A) = 0.6

P(offered position | college B) = 0.35

P(offered position | college C) = 0.25

P(offered position) = P(offered position | college A) * P(college A) + P(offered position | college B) * P(college B) + P(offered position | college C) * P(college C)

                              = 0.6 * 0.1 + 0.35 * 0.3 + 0.25 * 0.6

                              = 0.315

i) P(college A | offered position) = P(offered position | college A) * P(college A) / P(offered position)

                                                   = 0.6 * 0.1 / 0.315

                                                   = 0.1905

                                                   = 19.05%

ii) P(college B | offered position) = P(offered position | college B) * P(college B) / P(offered position)

                                                   = 0.35 * 0.3 / 0.315

                                                   = 0.3333

                                                   = 33.33%

ii) P(college C | offered position) = P(offered position | college C) * P(college C) / P(offered position)

                                                   = 0.25 * 0.6 / 0.315

                                                   = 0.4762

                                                   = 47.62%