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What is a probability model?
A mathematical description of a random process, including a sample space and the probability of each outcome.
Define 'sample space'.
The set of all possible outcomes of a random experiment.
What is the complement of an event?
All outcomes that are *not* part of the event.
Define probability.
A number between 0 and 1 that represents the likelihood of an event occurring.
What are equally likely outcomes?
Outcomes that have the same probability of occurring.
Formula for probability with equally likely outcomes?
$P(A) = \frac{\text{number of outcomes in event A}}{\text{total number of outcomes in the sample space}}$
Formula for the complement of an event E?
$P(E^c) = 1 - P(E)$
If a sample space S = {A, B, C}, what is P(S)?
P(S) = P(A) + P(B) + P(C) = 1
What is the range of values for any probability P(A)?
$0 \leq P(A) \leq 1$
How do you calculate the probability of not rolling a 4 on a six-sided die?
P(not 4) = 1 - P(4) = 1 - (1/6) = 5/6
Explain the concept of probability range.
Probabilities are always between 0 and 1, inclusive. 0 means impossible, and 1 means certain.
Explain the concept of the sum of all probabilities.
The probabilities of all possible outcomes in a sample space must add up to 1.
Explain how context is important when interpreting probabilities.
Probabilities should be explained in the context of the problem, using language like 'randomly selected' or 'chance'.
Explain the application of complement rule.
The complement rule is useful for calculating the probability of an event *not* happening, especially when dealing with phrases like 'at least' or 'at most'.
Explain the importance of sample space in probability.
Sample space is the foundation for calculating probabilities. It defines all possible outcomes, allowing us to determine the likelihood of specific events.