Probability Basics

Probability

Basic Concepts

• Experiment: An action or situation that can produce a set of outcomes.
• Sample Space: The set of all possible outcomes of an experiment.
• Event: A set of one or more outcomes of an experiment.

Probability Definitions

• Theoretical Probability: The probability of an event occurring based on the number of favorable outcomes divided by the total number of possible outcomes.
• Experimental Probability: The probability of an event occurring based on the frequency of the event occurring in repeated trials.

Rules of Probability

• Complement Rule: P(A') = 1 - P(A), where A' is the complement of event A.
• Addition Rule: P(A or B) = P(A) + P(B) - P(A and B), for events A and B that are not mutually exclusive.
• Multiplication Rule: P(A and B) = P(A) × P(B), for independent events A and B.

Types of Events

• Mutually Exclusive Events: Events that cannot occur simultaneously.
• Independent Events: Events where the occurrence of one event does not affect the probability of the other event.
• Conditional Probability: The probability of an event occurring given that another event has occurred.

Probability Distributions

• Discrete Probability Distribution: A probability distribution that assigns probabilities to distinct outcomes.
• Continuous Probability Distribution: A probability distribution that assigns probabilities to intervals of outcomes.

Key Concepts

• Random Variable: A variable whose possible values are determined by chance.
• Expected Value: The long-run average value of a random variable.

Probability

Basic Concepts

• An experiment is an action or situation that can produce a set of outcomes.
• A sample space is the set of all possible outcomes of an experiment.
• An event is a set of one or more outcomes of an experiment.

Probability Definitions

• Theoretical probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
• Experimental probability is based on the frequency of the event occurring in repeated trials.

Rules of Probability

• The Complement Rule states that the probability of an event not occurring is 1 minus the probability of the event occurring.
• The Addition Rule states that the probability of two events occurring is the sum of their individual probabilities minus the probability of their intersection.
• The Multiplication Rule states that the probability of two independent events occurring is the product of their individual probabilities.

Types of Events

• Mutually exclusive events are events that cannot occur simultaneously.
• Independent events are events where the occurrence of one event does not affect the probability of the other event.
• Conditional probability is the probability of an event occurring given that another event has occurred.

Probability Distributions

• Discrete probability distributions assign probabilities to distinct outcomes.
• Continuous probability distributions assign probabilities to intervals of outcomes.

Key Concepts

• A random variable is a variable whose possible values are determined by chance.
• The expected value is the long-run average value of a random variable.

Branches of Biology

• Botany is the study of plants, including their structure, growth, evolution, and interactions with the environment.
• Zoology is the study of animals, including their structure, behavior, evolution, and interactions with the environment.
• Microbiology is the study of microorganisms, such as bacteria, viruses, and fungi.
• Ecology is the study of the interactions between organisms and their environment.

Cell Biology

• A cell consists of a plasma membrane, cytoplasm, nucleus, mitochondria, ribosomes, lysosomes, and Golgi apparatus.
• Photosynthesis, respiration, metabolism, cell division (mitosis and meiosis), and cell signaling are important cellular processes.

Genetics

• Mendelian genetics involves laws of inheritance, including segregation, independent assortment, and dominance.
• Molecular genetics involves the structure and function of DNA, genes, and chromosomes, including the genetic code and mutations.

Evolution

• Mechanisms of evolution include natural selection, genetic drift, mutation, gene flow, and genetic variation.
• Evidence for evolution comes from the fossil record, comparative anatomy, molecular biology, and biogeography.

Biological Molecules

• Carbohydrates, including sugars, starches, and cellulose, function as energy storage and structural support molecules.
• Proteins, composed of amino acid chains, function as enzymes, hormones, and structural components.
• Lipids, including fats, oils, and steroids, function in energy storage and hormone regulation.
• Nucleic acids, including DNA and RNA, function in genetic information storage and transmission.