## 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!**

Tags: conditional, find, probability