How should I practice Coffee Rank Probability?

Start by reading the full statement, solve the visible examples, then compare the pattern against related Mercor phone screen problems in FastPrep.

Is Coffee Rank Probability associated with Mercor?

FastPrep tags this as a Mercor phone screen coding practice problem when the problem catalog has that company and stage context.

Coffee Rank Probability

Mercor● EasyFULLTIMEPHONE SCREEN

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Problem statement

The reported question buys two coffees from shop A and two from shop B and asks for the probability that both A coffees taste better than both B coffees.

For this exercise, generalize the numbers of coffees to positive countA and countB. Assume all individual quality scores are independent draws from the same continuous distribution, so ties have probability zero and every ordering of the distinct coffees is equally likely.

Compute the probability that every coffee from A has a strictly higher score than every coffee from B. Return the exact reduced fraction as a string numerator/denominator, with no spaces. The original two-and-two question is the input countA = 2, countB = 2.

Function

coffeeWinProbability(countA: int, countB: int) → String

Examples

Example 1

countA = 2countB = 2return = "1/6"

There are 4! equally likely labelled rankings. Exactly 2! * 2! put both A coffees above both B coffees, so the probability is 4/24 = 1/6.

Example 2

countA = 1countB = 2return = "1/3"

The one A coffee must be the highest of three equally likely ranks. The probability is 1/3.

Constraints

1 <= countA, countB <= 10.
All coffees are individually distinct, with independent identically distributed continuous quality scores.
Higher quality scores mean better taste; ties have probability zero.