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Binomial model for a delayed train on the days of a working week: expected number, exactly one day and at least one day

Binomial model for a delayed train on the days of a working week: expected number, exactly one day and at least one day

7 marks

A commuter travels to work by train on four days each week. On each of these days, independently, the probability that the train is delayed is \(\frac15\).

  1. Write down the expected number of days in one week on which the train is delayed.[2]

For one week, find the probability that the train is delayed

  1. on exactly one day;[2]
  2. on at least one day.[3]

Solution:

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Answer:(a) \(\dfrac45\) (b) \(\dfrac{256}{625}\) (c) \(\dfrac{369}{625}\)

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