Coding questions · ByteDance

Probability That One Fair Die Beats Another

Solve a coding interview problem about the probability that one fair die beats another when the dice may have different sizes and duplicate face values. The challenge emphasizes strict tie handling and an efficient approach that avoids comparing every possible pair of faces.

Two fair dice, A and B, are represented by integer arrays. Each array element is one physical face, so duplicate values are allowed and count as distinct, equally likely outcomes. The dice may have different numbers of faces.

Implement:

def solution(a: list[int], b: list[int]) -> float:

Return the probability, as a floating-point value, that a single roll of A is strictly greater than a single roll of B. Ties do not count.

Examples:

a = [1, 2, 3], b = [1, 2, 3] returns 3 / 9.
a = [2, 2], b = [1, 2] returns 2 / 4.

Assumptions:

Both arrays are non-empty.
Face values are integers.
Inputs may be large.
Your solution should avoid enumerating all len(a) * len(b) outcome pairs.

Probability That One Fair Die Beats Another

Constraints

Both dice contain at least one face
Face values are integers
Inputs may be large; avoid enumerating every ordered pair
Duplicate values represent distinct equally likely faces

Hints

For a fixed face value from A, count how many values in B are strictly smaller.
Sort one die, then use binary search for each face of the other die.