Playoff chase
Detroit has, remaining on their schedule, Green Bay, Baltimore and Green Bay again. To make the playoffs, they must beat Green Bay once, plus defeat Baltimore.
The chance of them winning the first game against Green Bay is 60%.
The chance of them beating Baltimore is 80%.
The chance of them winning the second game against Green Bay is also 60%.
What are their chances, in percent, of making the playoffs?
The answer is 67.2.
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1 solution
Moderator note:
Simple standard approach.
Divide the solution into 2 cases.
Case 1: They win the first game against Green Bay (60% chance.) Then if they defeat Baltimore (80% chance) they make the playoffs, otherwise they do not. Total percentage chance = 60% * 80% = 48%.
Case 2: They lose the first game against Green Bay (40% chance.) Then they need to win both remaining games (chance: 80% * 60% = 48%) to make the playoffs. Total percentage chance: 40% * 48% = 19.2 %.
Combining the two cases: Total playoff chance = 48% + 19.2% = 67.2%.