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MediumProbabilitypr-333

No Shared Birthday Probability

Problem

The probability that n people all have distinct birthdays among d equally likely days is prod_{i=0}^{n-1} (d - i) / d.

Given n and d (default 365), return the probability; return 0.0 when n > d.

Hint

Multiply the conditional probabilities of avoiding each previous birthday.

Test cases

case 1
in: [3,365]
expected: 0.9917958341152187
case 2
in: [2,4]
expected: 0.75
case 3
in: [5,3]
expected: 0
Starter codePython
def no_shared_birthday_probability(n, days=365):
    # Your code here
    pass

3 test cases · run your code against them in the editor