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What is the probability of an event?
The chance of the event occurring.
What is a probability experiment?
A process involving chance that leads to well-defined results called outcomes.
What is an outcome in a probability experiment?
The result of a single trial of a probability experiment.
What constitutes a sample space?
The set of all possible outcomes of a probability experiment.
Define classical probability.
Probability that uses sample spaces to determine the numerical likelihood of an event, assuming all outcomes are equally likely.
What is a simple event?
An event with only one outcome.
What is a compound event?
An event with more than one outcome.
What does the complement of an event E represent?
The set of outcomes in the sample space that are not in event E.
What is the range of probabilities?
The probability of any event E is a number between and including 0 and 1.
What does empirical probability rely on?
Actual experience to determine the likelihood of outcomes.
How can you express the probability of an event using its sample space?
P(E) = n(E) / n(S), where n(E) is the number of outcomes in E and n(S) is the total number of outcomes in the sample space.
Describe mutually exclusive events.
Two events that cannot occur at the same time and have no outcomes in common.
What is the formula for the probability of mutually exclusive events A and B?
P(A or B) = P(A) + P(B).
What is the formula for non-mutually exclusive events A and B?
P(A or B) = P(A) + P(B) - P(A and B).
What is the probability of independent events occurring together?
P(A and B) = P(A) × P(B).
Define dependent events.
Events where the occurrence of one event affects the probability of the other.
What is conditional probability?
The probability of an event B occurring given that event A has already occurred.
What is factorial notation?
A representation of the product of an integer and all the integers below it, denoted as n!.
What is a permutation?
An arrangement of n objects in a specific order.
How is a combination defined?
A selection of distinct objects without regard to order.
What is the formula for combinations?
nCr = n! / (r!(n - r)!) where r objects are selected from n objects.
How does the law of large numbers relate to probability?
It states that as the number of trials increases, the empirical probability approaches the theoretical probability.
What is the addition rule of probability used for?
To find the probability of compound events.
How can probabilities be visually represented?
Using Venn diagrams.
Why is it important to understand the concepts of probability in decision-making?
It helps assess risks and make informed choices based on the actual likelihood of events.
How many cards total are in a deck ?
There are 52 cards in a standard deck.
How many black cards are in a deck?
There are 26 black cards in a standard deck, consisting of 13 spades and 13 clubs.
