This is a contingency table and the question is if D is independent of A. Now I know that if they are, then P(A cap D)=P(A)*P(D)

Yazmin Sims 2022-10-17 Answered
Is my answer correct? Are these two events independent?
A B C 78 520 D 156 56
This is a contingency table and the question is if D is independent of A.
Now I know that if they are, then P ( A D ) = P ( A ) P ( D )
So in my case, P ( A D ) = 156 810
P ( A ) = 234 810
P ( D ) = 212 810
P ( A D ) = 0.19
P ( A ) P ( D ) = 0.07
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Answers (1)

bibliothecaqz
Answered 2022-10-18 Author has 12 answers
Your answer is correct, assuming that A and B are mutually exclusive and exhaustive and the same for C and D.
Another way to calculate would be to see if P ( D ) = P ( D | A )
P ( D ) = 212 810 = 0.262
P ( D | A ) = 156 234 = 0.667
Since P ( D ) P ( D | A ), D and A are not independant.
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