Question :
Justin, Cam, and Ben are playing a board game where exactly one player will win. Ben estimates that Justin has a 20%, percent chance of winning each game and that Cam has a 50%, percent chance of winning each game. What is the probability that Ben will win the board game?
Answer: 30%
Explanation:
Given the following :
Justin's chance of winning each game = 20%
Cam's chance of winning each game = 50%
Therefore, probability of :
Justin winning = 20/100 = 0.2
Cam winning = 50/100 = 0.5
Overall probability = 100% = 1
Therefore,
P(Justin winning) + P(Cam winning) + P(Ben winning) = 1
0.2 + 0.5 + P(Ben winning) = 1
P(Ben winning) = 1 - 0.7
P(Ben winning) = 0.3
0.3 = 30%