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If the probability of a bit error is p, what is the probability of a single, double, and triple error in a 10-bit word? Express it in terms of p.

Respuesta :

Answer:

  • single bit error: 10p
  • double bit error: 45p²
  • triple bit error: 120p³

Explanation:

The probability of n bits being in error is 10Cn × p^n, where ...

  10Cn = 10!/(n!(10-n!))

  10C1 = 10

  10C2 = 45

  10C3 = 120

This is the product of the probability that n bits can be in error and the number of ways that n bits can be chosen from the 10 in the word.

  n = 1: 10p

  n = 2: 45p²

  n = 3: 120p³

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