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A bag contains 5 red marbles and 10 blue marbles. Two marbles are drawn from the bag, one at a time, without replacement. What is a trial?

a. Pulling a single marble
b. Pulling two marbles, without replacement
c. The 15 marbles in the bag
d. Observing the color on the marble pulled

1 Answer

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Final answer:

In the context of drawing marbles from a bag without replacement, 'Pulling two marbles, without replacement' constitutes a single trial. This is because each draw affects the probability of the next within the same trial, as seen in scenarios where sequential draws alter the composition of marbles remaining in the bag.

Step-by-step explanation:

A trial is a basic unit of observation in a probability experiment; it's an action that results in a set of outcomes. In the context of drawing marbles from a bag, a trial can be defined in different ways depending on the design of the experiment.

If we consider the scenario presented in the question where two marbles are drawn from the bag, one at a time, without replacement, option b, 'Pulling two marbles, without replacement', would constitute a single trial since the outcome of interest includes both draws and their associated probabilities. This is consistent with the examples given, where each draw influences the probability of subsequent draws within the same trial.

For instance, if you have a bag containing marbles of different colors, and you draw a marble, record its color, and do not replace it, you have affected the makeup of the marbles remaining in the bag for the second draw. This sequential action without replacement is a defining feature of the trial in this type of probability problem. It is made clear by the examples where the probabilities on the second draw are altered based on the outcomes of the first draw.

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