## Mutually Exclusive Events in Probability

Consider a Stanley Cup playoff series in which the Toronto Male Leafs hockey team faces the Ottawa senators. Toronto hosts the first, second and if needed, fifth and seventh games in the best-of-seven contest. The Leafs have a %65 chance of beating the Senators at home in the first game. After that, they have a %60 chance of a win at home if they won the previous game, but a %70 chance if they are bouncing back from a loss. Similarly, the Leafs' chances of victory in Ottawa are %40 after a win and %45 after a loss.

B) CONSIDER THE FOLLOWING EVENTS =

A = (LEAFS LOSE THE FIRST GAME BUT GO ON TO WIN THE SERIES IN THE FIFTH GAME)

B = (LEAFS WIN THE SERIES IN THE FIFTH GAME)

C = (LEAFS LOSE THE SERIES IN THE FIFTH GAME)

IDENTIFY ALL THE OUTCOMES THAT MAKE UP EACH EVENT, USING STRINGS OF LETTERS SUCH AS LLSLL. ARE THERE ANY PAIRS FROM THESE THREE EVENTS MUTUALLY EXCLUSIVE?

C) What is the probability of event A in part B?

d) What is the chance of the Leafs winning in exactly five games?