5. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
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2. Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.
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3. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
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3. Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
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6. Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.
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1. (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
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6. (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
Alignment of the Resource to this Standard
IOER Community Rating: Not Rated