How to find conditional probability?

Question by : How to find conditional probability?
A little help…

A circuit to run a model railroad has 8 switches. Two are defective. If you select 2 switches at random and test them, find the probability that the second one is defective, given that the first one is defective.

I know conditional probability is P(A and B)/P(A), but for some reason, this problem is not making sense to me.

Best answer:

Answer by Billy
This is just a guess but:

P(2nd one of the two is defective|1st is defective)=P(both are defective)/P(1st is defective)=

the denominator is 2/8
the numerator (2/8)*(1/7)
thus, our quotient is 1/7 since the 2/8’s cancel out
We don’t use binomial distribution due to no replacement.

What do you think? Answer below!

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