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.

a) (6 pts) In what percent of games was the Golden Snitch caught?

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

won the match?

c) (1 pt) If you know that Hufflepuff won the match, what is the probability that the Golden was caught