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The probability of each trial resulting in a success is , where a 'trial' is a ball falling and a 'success' is the ball falling into the circle. The number of trials is , and we want the probability that the number of successes is greater than or equal to .
The formula that gives the probability of getting exactly successes in N trials is:and we shall need the sum of all the terms like this, for values of from to ; in other words:
And that's it.