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5 Flashcards

1
Q

What is probability?

A

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

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2
Q

What is the range of probability values?

A

Probability values range from 0 to 1.

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3
Q

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

A

It means the event is impossible.

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4
Q

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

A

It means the event is certain to occur.

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5
Q

What is an example of a probability of 0?

A

Rolling a 7 on a standard six-sided die.

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6
Q

What is an example of a probability of 1?

A

The sun will rise tomorrow.

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7
Q

What is a simple event?

A

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

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8
Q

What is a compound event?

A

A compound event consists of two or more simple events.

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9
Q

What is the formula for calculating probability?

A

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

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10
Q

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

A

0.5 or 50%.

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11
Q

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

A

1/6 or approximately 0.167.

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12
Q

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

A

True.

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13
Q

What is an independent event?

A

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

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14
Q

What is a dependent event?

A

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

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15
Q

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

A

4/52 or 1/13.

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16
Q

What does it mean to have a uniform probability distribution?

A

It means all outcomes are equally likely.

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17
Q

What is a biased coin?

A

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

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18
Q

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

A

3/6 or 1/2.

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19
Q

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

A

True.

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20
Q

What is the complement of an event?

A

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

21
Q

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

A

0.7.

22
Q

What is a sample space?

A

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

23
Q

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

A

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

24
Q

What is a probability tree?

A

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

25
Q

What does it mean if two events are mutually exclusive?

A

It means they cannot happen at the same time.

26
Q

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

A

2/6 or 1/3.

27
Q

What is conditional probability?

A

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

28
Q

What is the formula for conditional probability?

A

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

29
Q

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

A

False.

30
Q

What is the law of large numbers?

A

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

31
Q

What is expected value?

A

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

32
Q

How do you calculate expected value?

A

Multiply each outcome by its probability and sum the results.

33
Q

What is an example of a random variable?

A

The number of heads in 10 coin flips.

34
Q

What is a probability distribution?

A

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

35
Q

What is a normal distribution?

A

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

36
Q

What is a skewed distribution?

A

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

37
Q

What is the median in a probability distribution?

A

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

38
Q

What is a histogram?

A

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

39
Q

What is the range of a dataset?

A

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

40
Q

What is variance in probability?

A

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

41
Q

What is standard deviation?

A

Standard deviation is the square root of the variance.

42
Q

What is a binomial distribution?

A

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

43
Q

What are the parameters of a binomial distribution?

A

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

44
Q

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

A

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

45
Q

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

A

True.

46
Q

What is the difference between theoretical and experimental probability?

A

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

47
Q

What is a fair game in probability?

A

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

48
Q

What is a lottery in terms of probability?

A

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

49
Q

What is a roulette wheel?

A

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

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