I have a problem where you are testing $5$ parts, $3$ work and $2$ don't work, but you don't know which are which. If $X$ is the number of parts that have to be tested to figure out which ones don't work, what are the values of $P$ and their probabilities.
Okay, so I figured once you test either $2$ bad parts or $3$ good parts you can stop testing and that the max you would have to do is $4$ tests, because once you test $4$ you automatically know what the last one is. So, if
B denotes bad and
G denotes good then $X=2$ can be
BB, X=3 can be
GBB, and $X=4$ can be
BGGB which is $11$ total possibilities (I'm pretty sure this is all of them). This is kinda where I'm stuck though, I'm not really sure how to find $P(X=2,3,4)$.
Can anyone help?