Use properties of dependent probability like P(A | B) * P(B) = P(A and B) to solve some tricky probability problems!

Problem

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, left parenthesis, Q, right parenthesis, is 0, point, 9; the probability that they play hockey, P, left parenthesis, H, right parenthesis, is 0, point, 6.; and the probability that they play quidditch and hockey, P, left parenthesis, Q, space, a, n, d, space, H, right parenthesis, is 0, point, 5.
Based on this information, what is , the probability that a randomly selected student in the club plays quidditch, given that they play hockey, rounded to the nearest hundredth?
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • a percent, like 12, point, 34, percent
Get 3 answers correct in a row