Olympic Tryouts
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University of Maryland *
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392
Subject
Industrial Engineering
Date
Dec 6, 2023
Type
Pages
2
Uploaded by MinisterLyrebirdPerson844
Olympic_Tryouts
Problem Statement
An The US Olympic Committee is running try-outs for the 2022 Winter Olympics in Aspen, CO.
To qualify for the snowboard halfpipe team, a competitor needs to score at least 90 points from
the judges in this event. Three-time Olympian Shaun White knows that he performs poorly in
extremely warm or cold weather; specifically, he figures that he has a 9% chance of qualifying
(i.e., scoring at least 90 points) if the temperature is between 15F and 35F. In contrast, he thinks
his chance of qualifying is only 27% for temperatures below 15F and 18% for temperatures
above 35F. Three days before the event he checks the weather channel, who predicts that the
probabilities of temperatures below 15F is 8%, between 15F and 35F is 27%, and above 35F is
53%.
Givens
Scenario
Probability
qualifying 15-35 F
0.09
qualifying <15 F
0.27
qualifying >35 F
0.18
prob <15 F
0.08
prob 15-35 F
0.27
prob >35 F
0.53
A)
What is Shaun White's probability of qualifying for the 2022 Winter Olympics?
Method
𝑃 = 𝑃(𝑤𝑖?) = 𝑃(??𝑎?𝑖?𝑦𝑖??, 𝑎??) ∙ 𝑃(??????𝑎?????, 𝑎??)
Sample Solution
𝑃 = 𝑃(𝑤𝑖?) = (0.21 ∗ 17) + (0.20 ∗ 0.08) + (0.09 ∗ 0.75) = 0.1755
B)
His mom promises to throw a party provided that he qualifies and that the temperature is above
35F. What is the probability of this party being thrown?
Method
𝑃 = 𝑃(??𝑎?𝑖?𝑦𝑖??, > 35𝐹 ) ∙ 𝑃(??????𝑎?????, > 35𝐹)
Sample Solution
𝑃 = (0.18 ∗ 0.53) = 0.0954
C)
His uncle will throw a party either if Shaun qualifies or if the temperature is above 35F (if it's
warm outside, he figures they may as well). What is the probability of this happening?
Method
𝑃 = 𝑃(𝑤𝑖?) + 𝑃(𝑇 > 35𝐹) − 𝑃 (𝑤𝑖? ⋂ 𝑇 > 35𝐹)
Sample Solution
𝑃 = 0.1755 + 0.53 − 0.0954 = 0.6101
D)
His dad missed the event but read on the internet that his son had qualified. From his
perspective, what is the probability of the temperature having been between 15F and 35F?
Method
𝑃 = 𝑃(??𝑎?𝑖?𝑦𝑖??, 15 − 35𝐹 ) ∙ 𝑃(??????𝑎?????, 15 − 35𝐹)
Sample Solution
𝑃 = (0.09 ∗ 0.27) = 0.0243
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