A contest with 31 people

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Question from Kevin:

There is a contest with 31 people and only one winner each week.
We play for 17 weeks.
What are the odds of winning at least one week?
The chances of winning each week are independent from previous weeks.

Kevin,

There is a standard way to solve probability problems like this. It is based on the idea that if events are independent, the probability that they all happen is easy to find.

What is the probability of winning in a specified week?
What is the probability of NOT winning in that week?
What is the probability of not winning in week 1 AND not winning in week 2? [Answer - just multiply!]
What is the probability of not winning in ANY of 17 weeks?
What is the probability of NOT not-winning-in-any-week - that is to say, winning at least once?

Good Hunting!
RD

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.