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GIVEN:
2003 Season - Lane Stadium Seating Capacity = 66,000 ASSUMPTIONS: 5% participation in the SunCom trivia question The participants guess the answer to the trivia question There are 7 home games per year at Virginia Tech EQUATIONS: SOLUTION: Fans participating in the SunCom trivia question per game = 66,000 * 0.05 = 3,300 P(A) = Probability of reaching the SunCom operator = 1/3300 P(B) = Probability of guessing the answer to the question correctly = 1/4 P(A and B) = Probability of reaching the SunCom operator and guessing the answer to the question correctly Because the two events are independent of each other, their probabilities can be multiplied: P(A and B) = P(A) * P(B) = 1/3300 * 1/4 = 1/13200 The probability of reaching the SunCom operator and guessing the answer to the question correctly at ONE game = 1 in 13,200 However, there are 28 home games during the four years I was at Virginia Tech, therefore, the Cumulative Binomial Distribution is used to calculate the probability of reaching the SunCom operator and guessing the answer to the question correctly at least once during the 28 home games. B(x;n,p) = B(1;28;1/13200) = 1 in 472 However, I won the SunCom question twice already with a probability of: B(x;n,p) = B(2;28;1/13200) = 1 in 461,558 This means that the probability of winning the SunCom trivia quesiton at least twice while a student at Virginia Tech is approximately: 1 in a Half-a-Million INTERESTING FACTS: The chances of winning $100,000 in the VA Lotto Pick 5 (1 in 278,256) are better than winning the SunCom trivia question twice. If someone were to win the SunCom trivia question THREE TIMES (1 in 703 million), it would be the equivalent of winning the Mega Millions Jackpot (1 in 135 million) five times for at least $50 million. |
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