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Deciding whether it is binomially distributed

Deciding whether it is binomially distributed

IB Year 5 | Grade 11

For each of the experiments described below, \(X\) denotes the random variable 'the number of black marbles that are being drawn out of \(10\) trials'. State, giving a reason, whether \(X\) follows a binomial distribution.

  1. Experiment \(1\): A bag contains \(10\) black and \(20\) white marbles which are selected at random, one at a time with replacement.
  2. Experiment \(2\): This experiment is a repeat of Experiment \(1\) except that the bag contains \(10\) black, \(20\) white and \(30\) red marbles.
  3. Experiment \(3\): This experiment is a repeat of Experiment \(1\) except that marbles are not replaced after selection.

Solution:

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Answer:1. Yes, \(X\sim\mathrm{B}(10,\frac13)\). 2. Yes, \(X\sim\mathrm{B}(10,\frac16)\). 3. No: no replacement makes the trials dependent with changing conditional success probability.

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