Probability (P): A numerical measure between 0 and 1 that quantifies the likelihood of an event occurring; 0 indicates impossibility, 1 indicates certainty.
Experiment: A procedure or process that results in one outcome from a set of possible outcomes, used to observe random phenomena.
Sample Space (S): The complete set of all possible outcomes of an experiment; denoted as S.
Event: A subset of the sample space, representing one or more outcomes; can be simple (single outcome) or compound (multiple outcomes).
Conditional Probability (P(A|B)): The probability that event A occurs given that event B has already occurred, calculated as ( P(A|B) = \frac{P(A \cap B)}{P(B)} ).
Independence: Two events A and B are independent if the occurrence of one does not affect the probability of the other, i.e., ( P(A \cap B) = P(A) \times P(B) ).
1. What is a probability distribution?
2. What is the sample space in probability?
3. What is the primary role of conditional probability in probability analysis?
Probability — definition?
A measure of likelihood between 0 and 1.
Sample Space — role?
Contains all possible outcomes of an experiment.
Conditional Probability — mechanism?
Updates likelihood of an event given another has occurred.
Probability — definition?
Likelihood of an event occurring, between 0 and 1.
Sample space — role?
Contains all possible outcomes of an experiment.
Conditional probability — meaning?
Probability of A given B has occurred.
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