Statistics

A survey of undergraduate students in the School of Business at Northern University revealed the following regarding the gender and majors of the students:
Major
Gender Accounting Management Finance Total
Male 100 150 50 300
Female 100 50 50 200
Total 200 200 100 500

a. What is the probability of selecting a female student?
b. What is the probability of selecting a finance or accounting major?
e. What is the probability of selecting an accounting major, given that the person selected
is a male?

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1. There are a total of 1000 students. The number of women is 400.
a. 400/1000 = 0.400
b. (200+100)/1000 = 300/1000= 0.300
There are 600 males,so
c. 100/600 = 1/6 = 0.167

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2. a. What is the probability of selecting a female student? P(female accounting) + P (female Maj Mgmt) + P (Finance) = 0.2 + 0.1 + 0.1 = 0.4
b. What is the probability of selecting a Finance or Accounting major? P (Finance Male or Female) + P (Accounting Male or Female) = 0.2 + 0.4 = 0.6
c. What is the probability of selecting a female or an accounting major? Which rule of addition did you apply? General rule of addition, when events are NOT mutually exclusive. P(female) + P (accounting major) – P(female and accounting major) = 0.4 + 0.4 – 0.2 = 0.6.
d. Are gender and major independent? Why? No. Events are independent if the occurrence of one event does not affect the occurrence of another event (Lind, Chapter 5). The occurrence of gender in one major impacts gender is another major, given that the total number of students and gender ratio is fixed. For independent events P(A/B) = P(A), which is not the case here with gender/major.
e. What is the probability of selecting an accounting major, given that the person selected is a male? P(accounting | male) = P(Accounting and Male) / P(Male) = 100/500 x 500/300 = 100/300 = 0.33
f. Suppose two students are selected randomly to attend a lunch with the president of the university. What is the probability that both of those selected are accounting majors? P(A and B) = P(A) P(B)
Probability of first accounting student being selected for lunch = 200/500 = 0.4
Probability of second accounting student being selected for lunch = 199/499 = 0.399
Probability of first and second student being accounting = 0.4 x 0.399 = 0.1596

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