Suppose you are checking out the results from various Quidditch matches.

(Let's make it a unique tournament where all four Hogwarts houses compete at the same time.)

You find the percentage of times each house at Hogwarts won a match. Overall, 15% of matches

were won by Ravenclaw, 25% of matches were won by Gryffindor, 40% of matches were won

by Slytherin, and the remaining 20% of matches were won by Hufflepuff. You also note that in

games won by Ravenclaw, 40% of the time the Golden Snitch was caught. In games won by

Gry findor, 80% of the time the Golden Snitch was caught. In games won by Slytherin, 30% of

the time the Golden Snitch was caught. Finally, in games won by Hufflepuff, 60% of the time

the Golden Snitch was caught.

b) (6 pts) If you know the Golden Snitch was caught, what was the probability that Hufflepuff

won the match?