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