Probability - Interview Question Hi I recently got this question in an interview and would like help solving it. 

There were 2 boys and 3 girls in a room. A new baby entered the
room whose gender was unknown (but equally likely to be a boy/girl).
A nurse came into the room and picked one baby randomly and it
turned out to be a boy. What’s the probability that the new baby was
a boy?
Let $bg$ denote the event that the new child is a boy, and the randomly chosen child is then a girl. Label other events similarly viz. $P(bb)=P(bg)=\frac{1}{4},\,P(gb)=\frac{1}{6},\,P(gg)=\frac{1}{3}$. Then $$P(\text{new boy}|\text{boy chosen})=\frac{P(bb)}{P(bb)+P(gb)}=\frac{\frac{1}{4}}{\frac{1}{4}+\frac{1}{6}}=\frac{3}{5},$$where to simplify I've multiplied numerator and denominator by $12$.

As an existing answer that reached this value has been downvoted, I double-checked my answer with the Python here. In one run, the conditional probability estimate was $0.602380952381$, which is close enough to $0.6$ for the purposes of a sanity check.
I would like someone to verify this, since my confidence isn't high.
This is a method that helps corroborate chances. If something doesn't quite add up, you'd generally notice, since then one or more of the equations would be wrong.

cube chart

The description explains several events with 4 conditions; the chance a boy or a girl is added, and the chance the nurse picks a boy or a girl.

What you're asking is basically, what are the odds something happens, given that we know that thing already happened. In this case it's "What are the odds a boy was added, given that we know the nurse picked a boy". You can see the events cross together with the answer being $1/4$