In a set of 5 bottles,1 has a fracture.If you select a pair of bottles, probability that the fractured bottle is chosen is? Its also mentioned that this question is an example of Sampling without replacement
My question is , by the general method of how I do these kind of problems , I would assume that there are two possibilities


*

*You chose a defective bottle and then  a non defective which will have the probability of 
  1/5 X 4/4 = 4/20

    OR


*Choosing a non defective one first and then a defective one which will have the probability of
4/5 x 1/4 =4/20

Total probability is 8/20= 2/5 which doesn't make sense at all, since there is just one bottle to begin with
But the problem is I cant find a fault in my logic. Though I feel both the options are redundant , isn't both two different ways of selecting the pair?. Or is the fact that the phrase "one after the other" is absent a reason on why this might be a wrong approach?
    Thank you in advance


Here is another viewpoint.
Suppose you don't know there is a flawed bottle. You choose two of the five bottles. You are then told that one of the five bottles contains a crack. It is equally likely to be any of the five bottles, so each bottle has a probability of $\frac{1}{5}$ of being the cracked one.
You hold two bottles, so the probability of either one of them being the cracked one is $\frac{1}{5}+\frac{1}{5}=\frac{2}{5}$. Note that you can add these two probabilities because they are mutually exclusive events - they cannot both be cracked as there is only one cracked bottle.
Edit: I see now that JMP already briefly mentioned this at the end of his answer.
