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Binomial probabilities for the number of ones in ten random binary digits: two exact counts and a range of counts

Binomial probabilities for the number of ones in ten random binary digits: two exact counts and a range of counts

6 marks

A computer produces a string of \(10\) binary digits. Each digit is \(0\) or \(1\) with equal probability, independently of the other digits. Find the probability that the string contains

  1. exactly five \(1\)s;[2]
  2. exactly four \(1\)s;[1]
  3. four, five or six \(1\)s.[3]

Solution:

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Answer:(a) \(\dfrac{63}{256}\) (b) \(\dfrac{105}{512}\) (c) \(\dfrac{21}{32}\)

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