# Probability basics imported Flashcards

What are probability distributions?

Probability distributions are mathematical representations that describing the likelihood of each outcomes of a random experiment or process.

How are probability distributions expressed?

Probability distributions are expressed using mathematical functions or equations.

What is an example of a probability distribution?

An example is the binomial distribution, which models the number of successes in a fixed number of independent Bernoulli trials.

What do probability distributions reveal?

Probability distributions show the likelihood of each outcome occurring in a random experiment or process.

Can you provide an example of a uniform distribution?

Rolling a fair six-sided die has a uniform probability distribution.

In what scenarios are probability distributions used?

Probability distributions are used to describe events or processes involving randomness.

How are human heights modeled using distributions?

Human heights can be modeled using a normal distribution, with most people clustered around the average height.

How do probability distributions assign probabilities?

Probability distributions assign specific probabilities to each potential outcome.

Can you give an example of probability assignment?

Drawing a heart from a standard deck of cards has a probability of 1/4 (or 25%) because there are four suits, each equally likely.

What is the purpose of analyzing uncertainty?

Probability distributions enable us to estimate the likelihood of different events and outcomes in a structured manner.

What is an example of exclusive events?

Exclusive events are events that cannot happen simultaneously, meaning they are mutually exclusive. If one event occurs, the other cannot occur simultaneously. Example: Event A: Getting heads on a coin toss. Event B: Getting tails on a coin toss.

Could you provide example of exclusive events?

Event C: Rolling an odd number on a six-sided die. Event D: Rolling an even number on a six-sided die.

How can the probability of exclusive events be calculated?

For two exclusive events A and B, the probability of either event A or event B occurring is the sum of their individual probabilities: P(A or B) = P(A) + P(B)

C What are inclusive events and what’s an example?

Inclusive events are events that can happen simultaneously, either partially or completely. They may have overlapping outcomes. Example: Event E: It rains. Event F: It is cloudy.

Can you provide example of inclusive events?

Event G: Having an ice cream cone. Event H: Wearing sunglasses.

How is the probability of inclusive events calculated?

For two inclusive events E and F, the probability of event E or event F occurring is the sum of their individual probabilities minus the probability of both events occurring: P(E or F) = P(E) + P(F) - P(E and F) Note: The term “P(E and F)” represents the probability of both events E and F happening together.

What are independent events?

Independent events are events where the occurrence of one event does not affect the probability of the occurrence of another event. In other words, the outcome of one event has no influence on the outcome of the other event. Example: Event A: Flipping a coin and getting heads. Event B: Rolling a die and getting a 4.

Could you provide another example of independent events?

Event C: Choosing a card from a deck and getting a heart. Event D: Tossing a fair coin and getting heads.

How can the probability of independent events be calculated?

For two independent events A and B, the probability of both events occurring is the product of their individual probabilities: P(A and B) = P(A) × P(B)

What are dependent events and what’s an example?

Dependent events are events where the occurrence of one event affects the probability of the occurrence of another event. The outcome of the first event influences the outcome of the second event. Example: Event E: Drawing a colored marble from a bag (without replacement). Event F: Drawing another marble of a different color from the same bag.

Could you provide another example of dependent events?

Event G: Selecting a card from a deck and not replacing it. Event H: Selecting a second card from the deck after the first card was drawn.

How is the probability of dependent events calculated?

For two dependent events A and B, the probability of both events occurring is the product of the probability of the first event and the conditional probability of the second event given that the first event has occurred: P(A and B) = P(A) × P(B|A)

What is joint probability?

Joint probability refers to the probability of the intersection of two or more events, calculating the likelihood of both events occurring together.

Could you provide an example of joint probability?

Let’s consider two events related to rolling a fair six-sided die: Event A: Rolling an even number (2, 4, or 6). Event B: Rolling a number greater than 3 (4, 5, or 6).

How is joint probability calculated?

To calculate the joint probability of two events A and B, denoted as P(A and B), you can use the formula: P(A and B) = P(A) × P(B|A) Where: P(A) is the probability of event A occurring. P(B|A) is the conditional probability of event B occurring given that event A has occurred.

What is joint probability?

Joint probability refers to the probability of two or more events occurring simultaneously or together. It calculates the likelihood of the intersection of events happening at the same time.