How should I practice New 21 Game Probability?

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

Is New 21 Game Probability associated with UiPath?

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

New 21 Game Probability

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Problem statement

A player starts with 0 points and repeatedly draws an integer uniformly at random from 1 through maxPts, inclusive. The player stops drawing as soon as the score is at least k.

Return the probability that the final score is at most n.

Function

new21Game(n: int, k: int, maxPts: int) → double

Examples

Example 1

n = 10k = 1maxPts = 10return = 1.0

Every possible first draw is at most 10.

Example 2

n = 6k = 1maxPts = 10return = 0.6

Exactly six of the ten equally likely first draws finish at 6 or below.

Example 3

n = 21k = 17maxPts = 10return = 0.7327777870686082

Dynamic programming accumulates the probability of every reachable stopping score from 17 through 21.

Constraints

0 <= k <= n <= 10000
1 <= maxPts <= 10000
The result is accepted with absolute tolerance 1e-9.