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Greg in his video explanation for this question’s answer says that it is a counter intuitive result that the probability of pulling the purple marble remains the same irrespective of when it is drawn. In his explanation with the simple example however, he assumes that “the purple marble cannot come first.” This is true for this case because there are only 3 marbles and one purple marble in the 3. However, if there were more than one purple marble, then the probability of it being drawn in the second time would be affected by whether the first draw resulted in purple marble or another. If the first draw gave a purple marble, the second draw would have one less purple marble in the bag and therefore the probability would be different.
Am I missing anything in this? I cannot understand how this counterintuitive result is true. ChatGPT said I should think about this as though the draws have not occurred. Therefore, the probability of getting a purple marble in any drawn will remain the same. However, when I asked again it said the probability will depend on what marbles were drawn before the one we are interested in - and this makes more sense to me.
Please help,
Sincerely.