75% of all undergraduates are in the College, 10% are in Engineering, 8% are in Commerce, 4% are in Nursing, and 3% are in Architecture. In each school, the percentage of third years is as follows: 21% in the College, 25% in Engineering, 49% in Commerce, 57% in Nursing, and 33% in Architecture. If a randomly selected student is a third-year, what is the probability that they are in the College

the probability a randomly selected student is a third-year that they are in the College is 0.1743

Step-by-step explanation:

Given information

75% College = C = 0.75

10% are in Engineering, Eng = 0.1

8% are in Commerce, Com = 0.08

4% are in Nursing, Nurs = 0.04

3% are in Architecture, Arch = 0.03

21% Third year student = S = 0.21

21% in the College = 0.21

25% in Engineering = 0.25

49% in Commerce = 0.49

57% in Nursing = 0.57

33% in Architecture = 0.33

P (SlC) = 0.75 x 0.21 = 0.1575 is the probability of third year student in college

P (SlEng) = 0.1 x 0.25 = 0.025

P (SlCom) = 0.08 x 0.49 = 0.0392

P (SlNurs) = 0.04 x 0.57 = 0.0288

P (SlArch) = 0.03 x 0.33 = 0.0099

P (S) = P (SlEng) + P (SlCom) + P (SlNurs) + P (SlArch)

= 1 - (0.025 + 0.0392 + 0.0288 + 0.0099)

= 0.9031

The probability of third year student in college is

P (ClS) = P (SlC) / P (S)

= 0.1575 / 0.9031

= 0.1743