Syndrome Error Probability

Problem

A single-error-correcting block code of length n is sent over a binary symmetric channel with crossover probability p. The syndrome is zero exactly when zero or one bit flipped, so the probability of a nonzero syndrome is 1 - (1 - p)^n - n * p * (1 - p)^(n - 1). Return that probability.

Hint

Subtract the probabilities of exactly zero and exactly one flipped bit from one.

Test cases

case 1

in: [7,0.1]

expected: 0.14969439999999978

case 2

in: [3,0.5]

expected: 0.5

case 3

in: [7,0]

expected: 0

case 4

in: [7,1]

expected: 1

Starter codePython

def syndrome_error_probability(n, p):
    # Your code here
    pass

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