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 GGG
, BGB
, or GBB
, and $X=4$ can be BGGB
, GBGG
, GGBG
, GBGB
, GGBB
, or 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?