Binomial model for counters drawn with replacement: exactly two greens, at least one green and the expected number of greens

Binomial model for counters drawn with replacement: exactly two greens, at least one green and the expected number of greens

8 marks

A bag contains \(4\) green counters and \(20\) yellow counters. A counter is taken at random, its colour is recorded and it is then returned to the bag.

  1. This is done \(10\) times. Find the probability that a green counter is taken[6]
    1. exactly twice;
    2. at least once.
  2. The counter is taken and returned \(450\) times. Find the expected number of times that a green counter is taken.[2]

Solution:

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Answer:(a)(i) \(0.291\) (a)(ii) \(0.838\) (b) \(75\)

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