5 Flashcards
What is probability?
Probability is a measure of how likely an event is to occur.
What is the range of probability values?
Probability values range from 0 to 1.
If an event has a probability of 0, what does it mean?
It means the event is impossible.
If an event has a probability of 1, what does it mean?
It means the event is certain to occur.
What is an example of a probability of 0?
Rolling a 7 on a standard six-sided die.
What is an example of a probability of 1?
The sun will rise tomorrow.
What is a simple event?
A simple event is an outcome that cannot be broken down into simpler components.
What is a compound event?
A compound event consists of two or more simple events.
What is the formula for calculating probability?
Probability = Number of favorable outcomes / Total number of outcomes.
What is the probability of flipping a coin and getting heads?
0.5 or 50%.
What is the probability of rolling a 3 on a six-sided die?
1/6 or approximately 0.167.
True or False: The sum of probabilities of all possible outcomes equals 1.
True.
What is an independent event?
An independent event is one where the outcome does not affect the outcome of another event.
What is a dependent event?
A dependent event is one where the outcome is affected by the outcome of another event.
What is the probability of drawing an Ace from a standard deck of cards?
4/52 or 1/13.
What does it mean to have a uniform probability distribution?
It means all outcomes are equally likely.
What is a biased coin?
A biased coin is one that does not have an equal chance of landing on heads or tails.
What is the probability of rolling an even number on a six-sided die?
3/6 or 1/2.
Fill in the blank: The probability of an event A occurring is denoted as P(A).
True.
What is the complement of an event?
The complement of an event is the probability that the event does not occur.
If the probability of rain today is 0.3, what is the probability that it will not rain?
0.7.
What is a sample space?
A sample space is the set of all possible outcomes of an experiment.
What is an example of a sample space when rolling a die?
{1, 2, 3, 4, 5, 6}.
What is a probability tree?
A probability tree is a diagram that shows all possible outcomes of an event and their probabilities.
What does it mean if two events are mutually exclusive?
It means they cannot happen at the same time.
What is the probability of rolling a 1 or a 2 on a six-sided die?
2/6 or 1/3.
What is conditional probability?
Conditional probability is the probability of an event occurring given that another event has already occurred.
What is the formula for conditional probability?
P(A|B) = P(A and B) / P(B).
True or False: The probability of rolling a 5 on a die changes if you roll a 1 first.
False.
What is the law of large numbers?
The law of large numbers states that as the number of trials increases, the experimental probability will converge to the theoretical probability.
What is expected value?
Expected value is the average of all possible values of a random variable, weighted by their probabilities.
How do you calculate expected value?
Multiply each outcome by its probability and sum the results.
What is an example of a random variable?
The number of heads in 10 coin flips.
What is a probability distribution?
A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can take.
What is a normal distribution?
A normal distribution is a probability distribution that is symmetric about the mean.
What is a skewed distribution?
A skewed distribution is one where the data points are not symmetrically distributed.
What is the median in a probability distribution?
The median is the value that separates the higher half from the lower half of the data set.
What is a histogram?
A histogram is a graphical representation of the distribution of numerical data.
What is the range of a dataset?
The range is the difference between the highest and lowest values in the dataset.
What is variance in probability?
Variance measures how far a set of numbers are spread out from their average value.
What is standard deviation?
Standard deviation is the square root of the variance.
What is a binomial distribution?
A binomial distribution is a discrete probability distribution of the number of successes in a sequence of n independent experiments.
What are the parameters of a binomial distribution?
The number of trials (n) and the probability of success (p).
What is the probability of getting exactly k successes in n trials?
P(X = k) = (n choose k) * p^k * (1-p)^(n-k).
True or False: Probability can be expressed as a fraction, decimal, or percentage.
True.
What is the difference between theoretical and experimental probability?
Theoretical probability is based on the expected outcomes, while experimental probability is based on actual outcomes from trials.
What is a fair game in probability?
A fair game is one where all players have an equal chance of winning.
What is a lottery in terms of probability?
A lottery is a game of chance where winners are selected randomly from a pool of participants.
What is a roulette wheel?
A roulette wheel is a game of chance where players bet on where a ball will land on a spinning wheel.
