2.6.6 problem 65

(a)

All $(n+1)!$ permutations of the balls are equally likely, so the probability that we draw the defective ball is $\frac{1}{n+1}$ irrespective of when we choose to draw.

(b)

Consider the extreme case of the defective ball being super massive $(v>>\mathrm{nw})$. Then, it is more likely that a person draws the defective ball rather than a non defective ball, so we want to draw last. On the other hand, if $v$ is much smaller than $\mathrm{nw}$, then, at any stage of the experiment, drawing the defective ball is less likely than not, but after each draw of a non defective ball, the probability of it being drawn increases since there are less balls left in the urn. Thus, we want to be one of the first ones to draw.

So the answer depends on the relationship of $w$ and $v$.