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Binomial model for seeds that fail to germinate: the mean, an exact count and at least two failures

Binomial model for seeds that fail to germinate: the mean, an exact count and at least two failures

7 marks

Each seed of a certain variety, independently of the others, fails to germinate with probability \(0.06\). A gardener sows \(80\) of these seeds.

  1. Find the expected number of seeds that fail to germinate.[2]
  2. Find the probability that exactly five of the seeds fail to germinate.[2]
  3. Find the probability that at least two of the seeds fail to germinate.[3]

Solution:

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Answer:(a) \(4.8\) (b) \(0.180\) (c) \(0.957\)

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