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Question 1

What is probability?

Answer 1

Probability is a measure of how likely an event is to occur.

Question 2

What is the range of probability values?

Answer 2

Probability values range from 0 to 1.

Question 3

If an event has a probability of 0, what does it mean?

Answer 3

It means the event is impossible.

Question 4

If an event has a probability of 1, what does it mean?

Answer 4

It means the event is certain to occur.

Question 5

What is an example of a probability of 0?

Answer 5

Rolling a 7 on a standard six-sided die.

Question 6

What is an example of a probability of 1?

Answer 6

The sun will rise tomorrow.

Question 7

What is a simple event?

Answer 7

A simple event is an outcome that cannot be broken down into simpler components.

Question 8

What is a compound event?

Answer 8

A compound event consists of two or more simple events.

Question 9

What is the formula for calculating probability?

Answer 9

Probability = Number of favorable outcomes / Total number of outcomes.

Question 10

What is the probability of flipping a coin and getting heads?

Answer 10

0.5 or 50%.

Question 11

What is the probability of rolling a 3 on a six-sided die?

Answer 11

1/6 or approximately 0.167.

Question 12

True or False: The sum of probabilities of all possible outcomes equals 1.

Answer 12

True.

Question 13

What is an independent event?

Answer 13

An independent event is one where the outcome does not affect the outcome of another event.

Question 14

What is a dependent event?

Answer 14

A dependent event is one where the outcome is affected by the outcome of another event.

Question 15

What is the probability of drawing an Ace from a standard deck of cards?

Answer 15

4/52 or 1/13.

Question 16

What does it mean to have a uniform probability distribution?

Answer 16

It means all outcomes are equally likely.

Question 17

What is a biased coin?

Answer 17

A biased coin is one that does not have an equal chance of landing on heads or tails.

Question 18

What is the probability of rolling an even number on a six-sided die?

Answer 18

3/6 or 1/2.

Question 19

Fill in the blank: The probability of an event A occurring is denoted as P(A).

Answer 19

True.

Question 20

What is the complement of an event?

Answer 20

The complement of an event is the probability that the event does not occur.

Question 21

If the probability of rain today is 0.3, what is the probability that it will not rain?

Answer 21

0.7.

Question 22

What is a sample space?

Answer 22

A sample space is the set of all possible outcomes of an experiment.

Question 23

What is an example of a sample space when rolling a die?

Answer 23

{1, 2, 3, 4, 5, 6}.

Question 24

What is a probability tree?

Answer 24

A probability tree is a diagram that shows all possible outcomes of an event and their probabilities.

Question 25

What does it mean if two events are mutually exclusive?

Answer 25

It means they cannot happen at the same time.

Question 26

What is the probability of rolling a 1 or a 2 on a six-sided die?

Answer 26

2/6 or 1/3.

Question 27

What is conditional probability?

Answer 27

Conditional probability is the probability of an event occurring given that another event has already occurred.

Question 28

What is the formula for conditional probability?

Answer 28

P(A|B) = P(A and B) / P(B).

Question 29

True or False: The probability of rolling a 5 on a die changes if you roll a 1 first.

Answer 29

False.

Question 30

What is the law of large numbers?

Answer 30

The law of large numbers states that as the number of trials increases, the experimental probability will converge to the theoretical probability.

Question 31

What is expected value?

Answer 31

Expected value is the average of all possible values of a random variable, weighted by their probabilities.

Question 32

How do you calculate expected value?

Answer 32

Multiply each outcome by its probability and sum the results.

Question 33

What is an example of a random variable?

Answer 33

The number of heads in 10 coin flips.

Question 34

What is a probability distribution?

Answer 34

A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can take.

Question 35

What is a normal distribution?

Answer 35

A normal distribution is a probability distribution that is symmetric about the mean.

Question 36

What is a skewed distribution?

Answer 36

A skewed distribution is one where the data points are not symmetrically distributed.

Question 37

What is the median in a probability distribution?

Answer 37

The median is the value that separates the higher half from the lower half of the data set.

Question 38

What is a histogram?

Answer 38

A histogram is a graphical representation of the distribution of numerical data.

Question 39

What is the range of a dataset?

Answer 39

The range is the difference between the highest and lowest values in the dataset.

Question 40

What is variance in probability?

Answer 40

Variance measures how far a set of numbers are spread out from their average value.

Question 41

What is standard deviation?

Answer 41

Standard deviation is the square root of the variance.

Question 42

What is a binomial distribution?

Answer 42

A binomial distribution is a discrete probability distribution of the number of successes in a sequence of n independent experiments.

Question 43

What are the parameters of a binomial distribution?

Answer 43

The number of trials (n) and the probability of success (p).

Question 44

What is the probability of getting exactly k successes in n trials?

Answer 44

P(X = k) = (n choose k) * p^k * (1-p)^(n-k).

Question 45

True or False: Probability can be expressed as a fraction, decimal, or percentage.

Answer 45

True.

Question 46

What is the difference between theoretical and experimental probability?

Answer 46

Theoretical probability is based on the expected outcomes, while experimental probability is based on actual outcomes from trials.

Question 47

What is a fair game in probability?

Answer 47

A fair game is one where all players have an equal chance of winning.

Question 48

What is a lottery in terms of probability?

Answer 48

A lottery is a game of chance where winners are selected randomly from a pool of participants.

Question 49

What is a roulette wheel?

Answer 49

A roulette wheel is a game of chance where players bet on where a ball will land on a spinning wheel.