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. 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

a. Well, if we take a look at the total number of students, there are 500 in total, out of which 200 are female. So, the probability of selecting a female student would be 200/500, which simplifies to 0.4 or 40%.

b. Now, to determine the probability of selecting a finance or accounting major, let's add up the number of students in both majors. We have 100 accounting majors and 50 finance majors, which adds up to 150. So, the probability would be 150/500, which simplifies to 0.3 or 30%.

e. If we want to find the probability of selecting an accounting major, given that the person selected is a male, we need to look at the number of male accounting majors relative to the total number of male students. We have 100 male accounting majors out of a total of 300 male students, so the probability would be 100/300, which simplifies to 1/3 or approximately 0.3333.

a. To find the probability of selecting a female student, we need to divide the total number of female students by the total number of students.

Total number of female students = 200
Total number of students = 500

Probability of selecting a female student = Number of female students / Total number of students
= 200 / 500
= 0.4 or 40%

b. To find the probability of selecting a finance or accounting major, we need to add the number of students in the finance major and accounting major, and then divide it by the total number of students.

Number of students in finance major = 100
Number of students in accounting major = 200

Probability of selecting a finance major or accounting major = (Number of students in finance major + Number of students in accounting major) / Total number of students
= (100 + 200) / 500
= 300 / 500
= 0.6 or 60%

e. To find the probability of selecting an accounting major, given that the person selected is a male, we need to use the conditional probability formula.

Number of male students in accounting major = 100 (given)
Number of male students = 300 (given)

Probability of selecting an accounting major, given that the person selected is a male = Number of male students in accounting major / Number of male students
= 100 / 300
= 1/3 or 0.33 (rounded to two decimal places)

To find the probabilities, we will use the information given in the table.

a. Probability of selecting a female student:
To find the probability of selecting a female student, we need to divide the total number of female students (200) by the total number of students (500).
So, the probability of selecting a female student is 200/500, which simplifies to 2/5 or 0.4.

b. Probability of selecting a finance or accounting major:
To find the probability of selecting a finance or accounting major, we need to add the number of students in the finance major (100) and the number of students in the accounting major (200), and then divide it by the total number of students (500).
So, the probability of selecting a finance or accounting major is (100+200)/500, which simplifies to 3/5 or 0.6.

e. Probability of selecting an accounting major given that the person selected is male:
To find the probability of selecting an accounting major given that the person selected is male, we need to divide the number of male students in the accounting major (100) by the total number of male students (300).
So, the probability of selecting an accounting major given that the person selected is male is 100/300, which simplifies to 1/3 or 0.33.

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