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One or none? is a cooked quant interview question on probability.
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This is a medium-difficulty probability question that asks you to set up and solve a binomial equation. It's the kind of problem quant firms use to check whether you can translate a verbal constraint into a mathematical statement and then manipulate it cleanly.
The core skill being tested is comfort with binomial distributions and the ability to equate probabilities under different outcomes. Rather than computing a specific number, you're finding a parameter that satisfies a given condition. This requires you to write out the probability mass function for each case, set them equal, and solve—a workflow that appears frequently in interview problems and in the algebra underlying option pricing and risk models.