These are a few questions from my textbook which I am unsure of the answer I have come up with, any confirmation/help is appreciated!

(Click on the image and it will lead to image shack and then click on the image again to enlarge it)

Q1.

I picked d. This is because III implies that $\displaystyle Pr(A \cap D) = Pr(A) \times Pr(D)$ but you can't be alive and dead at the same time so $\displaystyle Pr(A \cap D) = 0 $ while $\displaystyle Pr(A) \neq 0 and Pr(D) \neq 0$ thus $\displaystyle Pr(A) \times Pr(D) \neq 0$. Is my reasoning correct?

Q2.

I picked d. This is because I implies that that $\displaystyle Pr(S \cap D) = Pr(S) \times Pr(D)$ but you can't be sick and dead at the same time so $\displaystyle Pr(S \cap D) = 0 $ while $\displaystyle Pr(S) \neq 0 and Pr(D) \neq 0$ thus $\displaystyle Pr(S) \times Pr(D) \neq 0$. III implies that $\displaystyle Pr(D|S) = Pr(D|H)$ which is not necessarily true. Thus II is the only correct choice left. Again I am unsure on my reasoning, confirmation would be appreciated!

Q3.

I am unsure of how to do this question... I am confused because if we assume the coin is a fair coin then Pr(Head) = Pr(Tail) and thus I. is true. However from the question if Ed only won 300 times out of 800 at Casino A means that $\displaystyle Pr(Win) = Pr(Head) = \frac{300}{800} = \frac{3}{8}$ and thus the coin is biased... Any ideas?

Thanks very much for any help!