Question

The US Olympic Committee is running try-outs for the 2018 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 30% chance of qualifying (i.e., scoring at least 90 points) if the temperature is between 15◦F and 35◦F. In contrast, he thinks his chance of qualifying is only 5% for temperatures below 15◦F and 10% for temperatures above 35◦F. Three days before the event he checks the weather channel, who predicts that the probabilities of temperatures below 15◦F is 40%, between 15◦F and 35◦F is 35%, and above 35◦F is 25%.

a) What is Shaun White’s probability of qualifying for the 2018 Olympics?

b) His mom promises to throw a party provided that he qualifies and that the temperature is above 35◦F. What is the probability of this party being thrown?

c) His uncle will throw a party either if Shaun qualifies or if the temperature is above 35◦F (if it’s warm outside, he figures they may as well). What is the probability of this happening?

Answer 1