General Probability Flashcards
What is the definition of probability?
Probability is a measure of the likelihood that an event will occur.
True or False: The probability of an event can be a negative number.
False
What is the probability of a certain event?
1
What is the probability of an impossible event?
0
Fill in the blank: The sum of probabilities of all possible outcomes of a random experiment is _____ .
1
What does it mean if two events are independent?
The occurrence of one event does not affect the probability of the other event.
What is the formula for calculating the probability of an event?
P(E) = Number of favorable outcomes / Total number of outcomes
What is the complement of an event A?
The event that A does not occur, denoted as A’.
True or False: The probability of event A and event B occurring together can be found by multiplying their individual probabilities if they are independent.
True
What is conditional probability?
The probability of an event occurring given that another event has already occurred.
What symbol is used to denote conditional probability?
P(A|B)
What is Bayes’ theorem?
A formula that describes how to update the probability of a hypothesis based on new evidence.
What is a random variable?
A variable whose possible values are numerical outcomes of a random phenomenon.
What are the two types of random variables?
Discrete and continuous random variables.
True or False: A discrete random variable can take on any value within a given range.
False
What is the expected value of a random variable?
The weighted average of all possible values the variable can take, weighted by their probabilities.
What is variance in probability?
A measure of how much the values of a random variable differ from the expected value.
What does the standard deviation represent?
The square root of the variance, indicating the amount of variation or dispersion in a set of values.
What is a probability distribution?
A function that describes the likelihood of obtaining the possible values that a random variable can take.
What is the difference between a probability mass function and a probability density function?
A probability mass function is used for discrete random variables, while a probability density function is used for continuous random variables.
What is a normal distribution?
A continuous probability distribution that is symmetric around its mean, depicting the distribution of many types of data.
True or False: In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean.
True
What is the law of large numbers?
The principle that as the number of trials increases, the experimental probability will converge to the theoretical probability.
What is a sample space?
The set of all possible outcomes of a random experiment.
What is a probability tree?
A graphical representation of the possible outcomes of a probability experiment, showing the probabilities of each outcome.
