Let a bowl contain 10 chips of the same size and shape. One and only one
of these chips is red. Continue to draw chips from the bowl, one at a time and at
random and without replacement, until the red chip is drawn.
Find the pmf of X, the number of trials needed to draw the red chip.
I thought about using the Bernoulli trial equation but I think that may be wrong to apply here. This problem is just confusing me and I'm not sure how to set a pmf like this us.
Best Answer
Hint: Continue to draw chips even after the red chip is drawn. This produces a uniform random ordering of the chips hence, by symmetry, the position $X$ of the red chip in the whole sample is uniformly distributed, that is, $P(X=k)$ does not depend on $k$ in $\{1,2,\ldots,10\}$. Can you finish?