How should I practice All Even Faces Before the First Odd Roll?

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

Is All Even Faces Before the First Odd Roll associated with IMC Trading?

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

All Even Faces Before the First Odd Roll

IMC Trading● EasyINTERNPHONE SCREEN

Learn

Problem statement

Roll a die repeatedly. Find the probability that every even-numbered face appears at least once before the first odd-numbered result.

For this exercise, assume the die is fair, has an even number sides of faces numbered consecutively from 1 through sides, and all rolls are independent. Repeated even results are allowed and do not reset the faces already observed. Stop at the first odd result; an odd result before every even face has appeared means failure.

For this exercise, assume sides is an input generalizing the conventional six-sided interpretation of the reported question. Complete allEvenBeforeOddProbability(sides) and return the event probability as a double without rounding.

For this exercise, assume answers are accepted when abs(actual - expected) <= 1e-9 * max(1, abs(expected)).

Function

allEvenBeforeOddProbability(sides: int) → double

Examples

Example 1

sides = 6return = 0.05

Under the stated conventional six-sided interpretation, ignore repetitions of previously seen even faces. The chances that the next new face is even are 3/6, 2/5 and 1/4. Their product is 1/20 = 0.05. This value is independently derived, rather than an author-confirmed answer.

Example 2

sides = 2return = 0.5

This authored example has only one even face. Success occurs exactly when the first roll is 2.

Example 3

sides = 4return = 0.16666666666666666

This authored example requires both 2 and 4 before 1 or 3. The probability is (2/4)*(1/3) = 1/6.

Constraints

For this exercise, assume 2 <= sides <= 20 and sides is even.
Each face has probability 1/sides on every independent roll.
Success requires all sides/2 distinct even labels before any odd result.