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?
a. = total female/grand total
b. = (total finance/grand total) + (total accounting/grand total)
When you want either-or probabilities, you need to add the individual probabilities.
e. This sounds like you want the male accounting majors out of the total males.
I hope this helps. Thanks for asking.
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
To answer these questions, we need to determine the probabilities based on the given information. Let's go through each question step by step:
a. The probability of selecting a female student can be calculated by dividing the number of female students by the total number of students. In this case, there are 200 female students out of a total of 500 students:
Probability of selecting a female student = Number of female students / Total number of students = 200 / 500 = 0.4
Therefore, the probability of selecting a female student is 0.4 or 40%.
b. The probability of selecting a finance or accounting major can be calculated by adding the number of students in these majors and dividing it by the total number of students. In this case, there are 200 accounting students and 100 finance students:
Probability of selecting a finance or accounting major = (Number of accounting students + Number of finance students) / Total number of students = (200 + 100) / 500 = 0.6
Therefore, the probability of selecting a finance or accounting major is 0.6 or 60%.
e. The probability of selecting an accounting major, given that the person selected is a male, can be calculated by dividing the number of male accounting students by the total number of male students. In this case, there are 100 male accounting students out of a total of 300 male students:
Probability of selecting an accounting major, given that the person selected is a male = Number of male accounting students / Total number of male students = 100 / 300 = 0.333
Therefore, the probability of selecting an accounting major, given that the person selected is a male, is 0.333 or 33.3%.