Colour of the first ball given a blue second

An urn holds $10$ balls: $3$ are green and $7$ are blue. Two balls are taken out one after the other, without putting the first back. You are told only that the second ball drawn is blue. Given this, what is the probability that the first ball drawn was green?

$1/3$. Draws without replacement are exchangeable, so conditioning on the second ball being blue is the same as conditioning on the first being blue. That leaves $3$ green among $9$ balls, giving $\tfrac39=\tfrac13$.