You are conducting a survey at a college with 800 students, 50 faculty members, and 150 administrators. Each of these 1,000 individuals has a single email address listed in the online campus directory. Suppose you were to select one email address at random. What is the probability it would be (a) a student, (b) a faculty member, (c) an administrator, (d) a faculty member or administrator, and (e) anyone except an administrator

a) 0.8

b) 0.05

c) 0.15

d) 0.2

e) 0.85

Step-by-step explanation:

a)

The probability of selecting student can be computed as

P (S) = number of students in survey/total number of individuals

P (S) = 800/1000=0.8

b)

The probability of selecting faculty member can be computed as

P (F) = number of faculty member in survey/total number of individuals

P (F) = 50/1000=0.05

c)

The probability of selecting administrator can be computed as

P (A) = number of administrator in survey/total number of individuals

P (A) = 150/1000=0.15

d)

The probability of selecting faculty member or administrator can be computed as

P (A or F) = P (A) + P (F) - P (A∩F) as A and F are mutually exclusive so P (A∩F) will be zero,

P (A or F) = P (A) + P (F) = 0.15+0.05=0.2

e)

The probability of selecting except administrator can be computed as

P (A') = 1-P (A) = 1-0.15=0.85