question archive The next two questions (1 and 2) refer to the following: The following five games are scheduled to be played at the World Curling Championships one morning
The next two questions (1 and 2) refer to the following: The following five games are scheduled to be played at the World Curling Championships one morning
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The next two questions (1 and 2) refer to the following:
The following five games are scheduled to be played at the World Curling Championships one morning. The values in parentheses are the probabilities of each team winning their respective game.
Game 1: Finland (0.43) vs. Germany (0.57)
Game 2: USA (0.28) vs.Switzerland (0.72)
Game 3: Japan (0.11) vs.Canada (0.89)
Game 4: Denmark (0.33) vs. Sweden (0.67)
Game 5: France (0.18) vs. Scotland (0.82)
1. The outcome of interest is the set of winners for each of the five games. How many outcomes are contained in the appropriate sample space?
(A) 5
(B) 10
(C) 25
(D) 32
(E) 64
2. In a sports game, the "favourite" is the team with the higher probability of winning and the "underdog" is the team that is less likely to win. What is the probability that at least one underdog wins their game?
(A) 0.93
(B) 0.74
(C) 0.80
(D) 0.67
(E) 0.59
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Answer:
1) In each game, no.of possibilities to select the winner is 2
Total no.of games=5
So, by multiplication rule,
No.of outcomes in the appropriate sample space = 2*2*2*2*2 = 25 = 32
2) Probability of atleast one underdog winning the game =1 - P(All favourites winning)
Therefore, probability = 1 - (0.57*0.72*0.89*0.67*0.82) = 1 - 0.2 = 0.8
So, probability of atleast one underdog winning the game = 0.8
