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Suppose that there exists a group of $400$ people and a group of $90$ people is chosen randomly (from the group of $400$). Suppose that person $X$ is a member of the group of $400$ people. What is the probability that $X$ belongs to the chosen group of $90$ people?

Would this be $\frac{\binom{399}{89}}{\binom{400}{90}}$?

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    Yes, but it's written more simply as just $\frac{90}{400} = \frac{9}{40}$. – 2017-02-14

1 Answers 1

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As said in the comments by @BrianTung:

You are looking here for a more complicated (yet correct) way to solve the problem.

If you have $90$ positive cases (the $90$ chosen people) and $400$ possible cases (the $400$ people you have): The probability that a randomly picked person is on the chosen one is simply $90 \over 400$.

Note that your answer gives the same result.