Question

Is gender independent of chosen major? Explain this matgematically!!

3. (7 points) Probability At a local university 100 different students in the accounting and economics majors answered a survey. It yielded the contingency table below, with 4 joint probabilities in the table, so that the joint probability that a student is female and an accounting major is 0.34 or 34%: Accounting Economics Major Major Female 0.34 0.10 Male 0.31 0.25 Hint: The first thing you should do is to label these categories as events A, A, B and B' a. What is the probability that a student is male? b. Given that an adult person is female, what is the probability that she is majoring in economics? 4.(5 points) Binomial Dintuil

Answer 1

Ans A)

Probability that student is male irrespective of discipline chosen by him equals to (0.31+0.25)/1=0.56

Ans B)

Now we have an information that adult person is female , now out of which probability that few females are learning Economics
P(Eco/Adult=Female)=Probability that given adult is female she learns economics

P(Eco ^ Female)/P(Female)=P(Eco/Adult=Female)

P(Eco ^ Female)=0.10

P(Female)=0.44

P(Eco/Adult=Female)=0.10/0.44=0.2272

Probability that given adult is female she learns economics
=0.2272

Answer 3)

We need to check whether gender and chosen major is independent that can be proved as below

If Probability(Major chosen | Gender)=Probability(Major chosen)*Probability(Gender)

Symbol " ^ " is intersection

Now,

Probability(Major chosen | Gender)= probability that certain major is chosen given gender of adult

Lets say Major chosen=Economics and Gender is Female. Therefore

Probability(Economics ^ Female)=0.10

Probability(Economics)=0.35 and Probability(Gender=Female)=0.44

Probability(Economics)*Probability(Gender=Female)=0.35*0.44=0.154

Probability(Economics ^ Female)=0.10<0.154=Probability(Economics)*Probability(Gender=Female)

Similarly we can check for other combination such as

Lets say Major chosen=Accounts and Gender is Male. Therefore

Probability(Accounts ^ Male)=0.31

Probability(Accounts)=0.65 and Probability(Gender=Male)=0.56

Probability(Accounts)*Probability(Gender=Male)=0.65*0.56=0.364

Probability(Economics ^ Female)=0.31<0.364=Probability(Economics)*Probability(Gender=Female)

Hence Major of specialization and gender both are dependent