What is the probability of someone winning the prize money during the 30-day run of the game?

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A commercial radio station is advertising a particular call-in game that will be played in conjunction with the introduction of a new product. The game is to be played every day for a period of 30 days. The game is only open to listeners between the ages of 15 and 30. Each caller will be the possible winner of one million dollars. The game runs as follows. At the beginning of each day the radio station randomly selects one date (day/month/year) from within a 15-year, span, that span consisting of the period from 15 to 30 years ago. Listeners whose birthday fall on the current day will be invited to call in to the station. At the end of the day, one listener will be chosen at random from among all of the listeners that called in that day. If that person’s birth date matches the predetermined date picked by the radio station exactly, he/she will win one million dollars. What is the probability of someone winning the prize money during the 30-day run of the game?

 

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