FACET SUMMARY FROM MOZART PROBLEM

Probability Facets
Back to facet modules. P01 Probability values

P010 Probabilities are between 0 and 1.

P017 A probability can be greater than 1.

P019 A probability can be negative.

P02 Probability for small sample space

Context: Given an experiment has a small number of outcomes, find the probability of an event.

P020 Student uses .

P024 All possible outcomes are listed.

P027 Typical outcomes are listed.

P029 No attempt to enumerate the sample space is made in any way.

P03 Combinations vs. Permutations

Context: Computing probabilities when the number of combinations and permutations are not equal (e.g., 1 head in 2 tosses).

P030 The student considers all ways (permutations) that the outcome can occur.

P033 Permutations are considered, but not computed or listed properly.

P039 The student only considers only one way (combination) for the event to occur.

P04 Experiment with n outcomes: equally likely

P040 If an experiment has n equally likely outcomes, the probability of any one of them is 1/n.

P049 If an experiment has n equally likely outcomes, the probability of any outcome is not necessarily 1/n.

P05 Experiment with n outcomes: not equally likely

P050a If an experiment has n outcomes, the probability of any one of them is not necessarily 1/n.

P050b If P(A)=k/n, then there were not necessarily n outcomes.

P058 If P(A)=k/n, then there were n outcomes.

P059 If an experiment has n outcomes, the probability of any one of them is 1/n.

P06 Random Selection of n items

P060 The probability of selecting any collection of n objects is equal to the probability of selecting any other collection of n objects.

P061 The probability of selecting any object is equal to the probability of selecting any other object.

P068 Any sample which is representative of the population is considered to be a random sample.

P069 A pseudo-random (e.g., haphazard or systematic) sample is considered to be a random sample.

P07 Interpretation of Probability

P070a The probability of a repeatable event is the frequency with which it occurs in the long run.

P070b Probability can be a subjective measurement of belief.

P075 To find the probability of an event, an experiment must be conducted many times to obtain the relative frequency.

P079 A probability less [greater than/equal to/less than] 0.5 means the event [will happen/is not predictable/will not happen] with certainty.

P08 Repeatable events

Context: An experiment is conducted n times and the number of times an outcome occurs is observed.

P080a As the number of trials of a random experiment increases, we expect the relative frequency to get closer to the event probability

P080b If you conducted an experiment k times and observed event A k times, the probability of A occurring on the next trial is approximately k/n.

P081 Probability predicts outcomes, but does not determine outcomes.

P088 Probability cannot be estimated based on past performance.

P089 If you conducted an experiment k times and observed event A k times, the probability of A occurring on the next trial is exactly k/n.

P09 Expected value of a binomial random variable

Context: Given n Bernoulli trials that occur with probability p, what happens to the expected number of successes as n increases?

P090 As the number of trials increases, the probability of observing the expected number decreases.

P097 As the number of trials increases, the probability of observing the expected number does not change.

P099 As the number of trials increases, the probability of observing the expected number increases.

P10 Complimentary events given a frequency distribution

Context: Given a frequency distribution on 0,1,…, compute or similar type event requiring complements. Also, given n independent Bernoulli trials that occur with probability p, compute the probability of at least k successes or at most k successes.