Pairwise Independence $\neq$ Mutual Independence

Consider the events $X=\text{tails}$ and $Z=1$ . Then, $P(X=\text{tails} \cap Z=1)=0,$ since $Z$ cannot be 1 if $X$ is tails. On the other hand, $P(X=\text{tails})=1/2$ and $P(Z=1)=1/4$ . A simple computation shows that $P(X=\text{tails} \cap Z=1)=0\neq P(X=\text{tails})\cdot P(Z=1)$ , so these two events are not independent. It follows then that $X$ and $Z$ are not independent, and a similar argument shows that $Y$ and $Z$ are not independent either. Thus, the last three statements are all false.

On the other hand, it is given in the problem statement that $X$ and $Y$ are independent, so the first statement is true. The answer then, is 1.