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Case Study on Probability

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Case Study

1. Introduction:

Great Air Commuter Service is a small regional airline. Provides commuter service between Boston and New York –three round trips daily (total of six flights per day). Promotional contest awarding a large prize to be run one day per month on each flight. The day each month for contest to be run will be selected randomly on the first of each month. On each flight that day, all passengers will write down their birthday (month and day). If any two people on the plane have the same birthday, they will place their names in a hat and one name will be selected to receive the grand prize. Capacity of each flight is a maximum of 40 passengers (plus crew). The marketing director believes there is a very low chance of a birthday match, so only a small chance of giving away the large prize. Marketing director states that the probability for a match will be 40/365 (10.95%) for a full plane and less than that when there are fewer than 40 passengers on board.

11. Statement of the Problem: 1. What is the probability of one or more birthday matches on flights of 20, 30,or 40 passengers? 2. With six flights daily (carrying the same number of passengers: 20, 30, and 40), what are the chances that Great Air Commuter Service will end up awarding two or more major prizes during a given month?

111. Methodology

* Calculation of mutually exclusive events

1V. Solution: *Assumptions: * Leap year * Twins * Seasonality of births ***There are 365 birthdays equally likely P (A) =The probability of at least two passengers having the same birthday: P (A) = #of ways for event to occur Total # of possible outcome The Complement of event A: P (A’) =The probability of there are not being

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