<p>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.</p>
<ol class="num-list"><li><div class="list-item-content"><span class="list-item-text">Experiment \(1\): A bag contains \(10\) black and \(20\) white marbles which are selected at random, one at a time with replacement.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Experiment \(2\): This experiment is a repeat of Experiment \(1\) except that the bag contains \(10\) black, \(20\) white and \(30\) red marbles.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Experiment \(3\): This experiment is a repeat of Experiment \(1\) except that marbles are not replaced after selection.</span></div></li></ol>

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.

Experiment \(1\): A bag contains \(10\) black and \(20\) white marbles which are selected at random, one at a time with replacement.

Experiment \(2\): This experiment is a repeat of Experiment \(1\) except that the bag contains \(10\) black, \(20\) white and \(30\) red marbles.

Experiment \(3\): This experiment is a repeat of Experiment \(1\) except that marbles are not replaced after selection.

Deciding whether it is binomially distributed

Deciding whether it is binomially distributed