A survey of a sample of business students resulted in the following information

Question

A survey of a sample of business students resulted in the following information regarding the genders of the individuals and their selected major:

Enter the probability that a randomly selected business student is a management major, given that the student is female in blank #1. (Round your answer to 2 decimal places and enter your answer as 0.24 and not as .24.)

Enter the probability that a randomly selected business male student is an accounting major in blank #2.   (Round your answer to 2 decimal places and enter your answer as 0.24 and not as .24.)

Enter the probability that a randomly selected marketing student is female blank #3. (Round your answer to 2 decimal places and enter your answer as 0.24 and not as .24.)

Are the events "female" and "accounting" independent? Enter your answer (yes or no) in blank #4.

Gender Management Marketing Accounting Total Male 40 10 30 80 Female 30 20 70 120 Total 70 30 100 200

Explanation / Answer

Enter the probability that a randomly selected business student is a management major, given that the student is female in blank #1.

Answer : P(Management Major) = Number of management major student / Number of students = 70/200 = 0.35

Enter the probability that a randomly selected business male student is an accounting major in blank #2.

Answer : Pr (Accounting Major l Male student) = NUmber of accounting major student who are male/ Number of total male students = 30/ 80 = 0.375

Enter the probability that a randomly selected marketing student is female blank

Answer : Pr (Female l Marketing student) = Number of female student in marketing major / NUmber of marketing major student = 20/ 30 = 0.667

Events female and accounting are independent, if,

Pr ( Female and accounting) = Pr (Female) * Pr( Accounting)

Pr(Female and accounting) = 70/200 = 0.35

Pr (Female) = 120/200 = 0.6

Pr( Accounting) = 100/200 = 0.5

so Pr(Female) * Pr( Accounting) = 0.6 * 0.5 = 0.3

so this two values are not same so both events are not independent. So, the answer is NO.

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