10MAT Probability Revision. Flashcards by Brad Bridges

What is probability?

Probability is the measure of the likelihood that an event will occur.

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What is the probability of an event that is certain to happen?

1 or 100%

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What is the probability of an impossible event?

0 or 0%

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What is a sample space?

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

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Define a simple event.

A simple event is an event that consists of a single outcome.

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What is a compound event?

A compound event is an event that consists of two or more simple events.

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True or False: The sum of probabilities of all outcomes in a sample space equals 1.

True

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What is the formula for calculating the probability of an event?

P(E) = Number of favorable outcomes / Total number of outcomes

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What does it mean if two events are independent?

Two events are independent if the occurrence of one does not affect the occurrence of the other.

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What does it mean if two events are mutually exclusive?

Two events are mutually exclusive if they cannot occur at the same time.

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If P(A) = 0.4 and P(B) = 0.3, what is P(A or B) if A and B are mutually exclusive?

P(A or B) = P(A) + P(B) = 0.7

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What is the complement of an event?

The complement of an event is the event that represents all outcomes not in the event.

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If P(A) = 0.6, what is P(not A)?

P(not A) = 1 - P(A) = 0.4

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What is a probability tree diagram?

A probability tree diagram is a visual representation of all possible outcomes of a probability experiment.

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How do you calculate the probability along a branch of a tree diagram?

Multiply the probabilities along the branch.

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What is the total probability rule?

The total probability rule states that the total probability of an event is the sum of the probabilities of all disjoint events leading to it.

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What is conditional probability?

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

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How is conditional probability denoted?

P(A | B), which reads as the probability of A given B.

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What is the multiplication rule for independent events?

P(A and B) = P(A) * P(B) for independent events.

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What is the formula for conditional probability?

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

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What does a tree diagram represent?

A tree diagram represents all possible outcomes of a sequence of events.

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True or False: The branches of a tree diagram must add up to 1.

True

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What is expected value?

Expected value is the average outcome of a probability experiment over a large number of trials.

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How do you calculate expected value?

E(X) = Σ [x * P(x)], where x is an outcome and P(x) is its probability.

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What is a discrete random variable?

A discrete random variable is a variable that can take on a countable number of distinct values.

Fill in the blank: The probability of getting heads in a fair coin toss is ___ .

0.5

What is the range of probability values?

0 to 1

If you roll a six-sided die, what is the probability of rolling a 4?

1/6

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

4/52 or 1/13

What is the formula for the probability of the union of two events?

P(A or B) = P(A) + P(B) - P(A and B)

True or False: The probability of drawing a heart or a diamond from a deck of cards is 1/2.

True

What is the probability of flipping three heads in a row with a fair coin?

1/8

What is the total number of outcomes when flipping a coin twice?

What is a Venn diagram?

A Venn diagram is a visual representation used to show the relationships between different sets.

If P(A) = 0.5 and P(B) = 0.4, what is P(A and B) if A and B are independent?

0.2

What is the probability of getting at least one head when flipping a coin twice?

3/4

What does it mean if an event has a probability of 0.7?

The event is likely to occur.

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

1/3

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

1/4

What does it mean for outcomes to be equally likely?

Each outcome has the same chance of occurring.

What is the probability of getting a sum of 7 when rolling two dice?

6/36 or 1/6

True or False: The probability of an event can exceed 1.

False

If you have a bag with 3 red balls and 2 blue balls, what is the probability of drawing a red ball?

3/5

What is a probability distribution?

A probability distribution describes how probabilities are distributed over the values of a random variable.

What is a binomial probability?

A binomial probability is the probability of achieving a fixed number of successes in a fixed number of independent Bernoulli trials.

What is the formula for binomial probability?

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

What is the expected number of successes in a binomial distribution?

np, where n is the number of trials and p is the probability of success.

What is the variance of a binomial distribution?

np(1-p)

What does a normal distribution look like?

A bell-shaped curve.

What is the mean of a normal distribution?

The center of the distribution.

What is the standard deviation in a normal distribution?

A measure of the spread of the distribution.

What is the empirical rule?

The empirical rule states that for a normal distribution, approximately 68% of data falls within one standard deviation of the mean.

What is the z-score?

The z-score indicates how many standard deviations an element is from the mean.

What is the formula for calculating a z-score?

z = (X - μ) / σ

What is the probability of selecting a blue ball from a bag with 5 blue and 3 green balls?

5/8

What is a dependent event?

A dependent event is an event whose outcome is affected by the outcome of another event.

True or False: The probability of two independent events occurring is the sum of their probabilities.

False

If P(A) = 0.2 and P(B) = 0.5, what is P(A or B) if A and B are not mutually exclusive?

P(A or B) = P(A) + P(B) - P(A and B)

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

3/6 or 1/2

What is the probability of drawing a face card from a standard deck of cards?

12/52 or 3/13

What is the outcome of a probability experiment?

The result of a single trial of the experiment.

What is the law of large numbers?

The law of large numbers states that as the number of trials increases, the empirical probability approaches the theoretical probability.

What is the difference between theoretical probability and experimental probability?

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

What is the probability of getting tails in a single coin toss?

1/2

What is the probability of rolling a number greater than 4 on a six-sided die?

1/3

What is the total number of outcomes when rolling two dice?

What is the probability of not rolling a 1 on a six-sided die?

5/6

What is the expected value of rolling a fair six-sided die?

3.5

What is the probability of flipping a coin and rolling a die, getting heads and a 3?

1/12

What is the probability of drawing two aces in a row from a standard deck of cards without replacement?

4/52 * 3/51 = 1/221

What does it mean to sample with replacement?

Sampling with replacement means that after an item is selected, it is returned to the sample space.

What is the probability of getting a sum of 10 when rolling two dice?

3/36 or 1/12