Probability measures the likelihood of an event occurring, expressed as a number between 0 and 1. It is often used to predict outcomes in various scenarios.
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The probability of an event A is calculated using $P(A) = \frac{n(A)}{n(S)}$ where $n(A)$ is the number of favorable outcomes and $n(S)$ is the total number of possible outcomes.
The sum of probabilities for all possible outcomes in a sample space equals 1.
For any event A, the probability ranges from 0 (impossible event) to 1 (certain event).
The complement rule states that $P(\text{not } A) = 1 - P(A)$.
In mutually exclusive events, if A and B cannot occur at the same time, then $P(A \cup B) = P(A) + P(B)$.
Review Questions
How do you calculate the probability of a single event?
What does it mean if an event has a probability of zero?
Explain what mutually exclusive events are and how their probabilities are related.
Related terms
Sample Space: The set of all possible outcomes in a probability experiment.
Complementary Events: Events where one occurs if and only if the other does not; represented as $P(\text{not } A) = 1 - P(A)$.
Mutually Exclusive Events: Events that cannot occur at the same time; their combined probability is $P(A \cup B) = P(A) + P(B)$.