Answer:
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
