A sports club at a school offers students the opportunity to play five sports over the course of the school year: basketball, soccer, football, hockey, and quidditch. Members of the club are allowed to play as many sports as they like.
Let $Q$ represent the event that a student in the club plays quidditch and $H$ represent the event that they play hockey.
Given a randomly selected student in the club, the probability that they play quidditch, $P(Q)$, is $0.9$; the probability that they play hockey, $P(H)$, is $0.6$.; and the probability that they play quidditch and hockey, $P(Q\text{ and }H)$, is $0.5$.
**Based on this information, what is $P(Q\text{ | }H)$, the probability that a randomly selected student in the club plays quidditch, given that they play hockey, rounded to the nearest hundredth?** [[☃ input-number 1]]