Hi guys, I'm back again with another question hopefully you guys can help me.

[Question]

We have a fuse box with 20 fuses, 5 of which are defective.

If 2 fuses are selected at random, in succession, and without replacement, what is

the probability that both fuses are defective?

[SOLN]

A = "1st fuse is defective", P(A) = 5/20 = 1/4

B = "2nd fuse is defective", P(B) = 4/19

P(A n B) = (1/4) * (4/19) = 1/19

? - My confusion has to do with independence, since you can't calculate P(B|A) without having P(A n B)

and since the above solution only seems to be calculable if you know the events are independent. Since then P(B|A) = P(B).

But it seems to me that the events would be dependent since there is no replacement. For instance if the first fuse chosen

was not defective then wouldn't the probability of choosing a defective fuse on the 2nd try actually be 5/19?

I guess then my actual question is how can I figure out whether or not the events are dependent if (A n B) is not known?

I hope I am making some sort of sense.

Thanks for your help guys, I sure need it.