Counting N for an Unfair Coin

What this binomial distribution interview question tests

This is an easy probability question that asks you to work backwards from distributional constraints to recover unknown parameters. It's the kind of problem quant interviews use to check whether you can manipulate the binomial distribution fluently and set up systems of equations from given information.

The core skill is recognizing that the expected value of a binomial random variable and the ratio of consecutive probability mass function values both encode information about n and p. You'll need to use both constraints together: one pins down the relationship between the parameters directly, while the other gives you a second equation. The algebra is straightforward once you've set up the system correctly.

• Expected value of binomial distributions
• Probability mass function ratios and simplification
• Solving simultaneous equations for unknown parameters