Question: A new weight reduction program is to be tested on N overweight people. They were each weighed before starting the program. After one month, they were weighed again. It was observed that k of these lost weight. Now, weight does not remain constant, and one might assume that if the program did not work, a person’s weight is equally likely to go up as go down during the month.

1. Assuming that the program had no effect whatsoever, what is the probability that at least k of these people lost weight?

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