Question

Very Happy Fairly Happy Fairly Unhappy Very Unhappy Total
Male 501 619 287 103 1510
Female 349 620 116 99 1184
Total 850 1239 403 202 2694

The table shows results from a survey for married adults classified by gender and level of happiness. For these subjects, are the events being very happy and being a female independent?
A) Yes; P(Female) = P(Very Happy|Female)
B) Yes; P(Female) = P(Female|Very Happy)
C) No; P(Female) ≠ P(Very Happy|Female)
D) No; P(Very Happy) ≠ P(Very Happy|Female)

Answer 1

P(Female)=1184/2694=0.44

P(V happy)=850/2694=0.32

P(Female | V happy)=349/850=0.41

P(V happy | Female)=349/1184=0.29

So ans is D P(Very Happy) ≠ P(Very Happy|Female) 

Answer 2

Here, Total person = 2694

Number of very happy = 850
So, Relative frequency = 850/2694 = 0.315

As it is a finite value, Not in major, not in majority, so it's not very happy.

Female data contributes equally as male's. They are quite linear function with proper differences.

In short, Your Answer would be:Option D) No; P(Very Happy) ≠ P(Very Happy|Female)

Hope this helps!