Probability of second cupcake being chocolate given first is chocolate

[firstwave]

Probability Question - Need help please!

There are three boxes with 2 cupcakes in each one of them:

First box: 2 chocolate cupcakes
Second box: 1 chocolate, 1 vanilla
Third box: 2 vanilla cupcakes

A person randomly opens up a box and selects one cupcake. It is a chocolate cupcake. She then pulls out the remaining cupcake in the same box. What is the probability that it is a chocolate cupcake?

Ok here is what I think...
Since the question is only asking for the probability that the second cupcake in the box is chocolate, we don't have to worry about the first step of picking the right box. Therefore, the probability should be 1/2 because you can either pick a vanilla or a chocolate, but it doesn't really sound convincing...

 

[EnumaElish]

There are three boxes with 2 cupcakes in each one of them:

First box: 2 chocolate cupcakes
Second box: 1 chocolate, 1 vanilla
Third box: 2 vanilla cupcakes

A person randomly opens up a box and selects one cupcake. It is a chocolate cupcake. She then pulls out the remaining cupcake in the same box. What is the probability that it is a chocolate cupcake?

It's a conditional prob. question, "what is the prob. of the box being the choc. box given a choc cake has been picked?"

P(Choc box|a choc cake has been picked) = P(Choc box and a choc cake has been picked)/P(a choc cake has been picked) = P(Choc box)/(3/6) = (1/3) / (1/2) = 2/3.

See this example.