AP Statistics Chapter 5 Review

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What is probability?

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28 Terms

1

What is probability?

The percentage of times an outcome would occur in a very long series of trials is between 0 and 1.

Note: Probability is not accurate in the short run.

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2

What is a random process?

Outcomes that are determined purely by chance.

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3

What is the Law of Large Numbers?

If we observe more and more trials of any random process, the proportion of times that a specific outcome occurs approaches its probability.

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4

How do you interpret the Law of Large Numbers in CONTEXT?

In a long sequence of a randomly selected _____, the estimated proportion of them ___ is (probability)

Example: In a long sequence of a randomly selected Lakeview resident, the proportion of them being a Cubs fan is 44%.

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5

What is a simulation?

Imitates a random process in a way that simulated outcomes are consistent with real-world outcomes.

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6

How do you use a random didgets table?

Step 1 (State): State what youā€™re being asked. (Examples are below)
Step 2 (Plan): Select random integers 1-4 until 4 prizes are represented (and the amount of times it takes to get all 1, 2, 3, and 4).

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7

What is a sample space?

The set of all possible outcomes of a chance process (always adds up to 1).

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8

What is a probability model?

A chance process that consists of two parts: A sample space (s) and a probability for each outcome.

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9

What is an event?

A collection of outcomes from a chance process. (EX: They pass their class)

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10

What is a complement?

The other outcome of an event

EX: The event is they pass their class, the complement is that they donā€™t pass their class)

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11

What does Mutually Exclusive mean (important).

Two events are mutually exclusive if they have no outcomes in common and can never occur together.

P(A & B) = 0

MEANS YOU CAN ADD THEM.

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12

What is the complement rule?

P(A^c) = 1-P(A)

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13

What is the General Addition Rule? (Give definition and actual rule)

If A and B are any two events resulting from some chance process.

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

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14

What does an Intersection mean?

The intersection of events A and B (Denoted by upside-down U) refers to the occurrence of two events at the same time. MEANS ā€œANDā€// OVERLAP

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15

What does Union Mean?

Union of events A and B (denoted by U) means all of the outcomes in A OR B OR both. MEANS TO COMBINE; THINK ā€œandā€ ā€œorā€

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16

What is Conditional Probability?

The probability that one event happens given the other event happening.

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17

What is the conditional probability formula?

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

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18

What is the General Multiplication Rule?

If A and B are any two events resulting from some chance process, then:

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

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19

What does Independent Mean?

If the occurrence of one event does not change the probability that the other event will happen. (EX: Coin flips)

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20

What is the Independent Formula?

P(A|B) = P(A)

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21

How do you know something is independent?

If P(A|B)=P(A)

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22

What is the Multiplication Rule for Independent Events?

If A and B are independent events, then the probability that A and B both occur is:

P(A and B) = P(A)*P(B)

OR

P(A and B and Cā€¦) = P(A)*P(B)*P(C)ā€¦

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23

When are you allowed to use this: P(A and B) = P(A)*P(B)?

If they are independent.

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24

When are you allowed to use this: P(A or B) = P(A U B) = P(A)+P(B)?

If they are mutually exclusive.

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25

When using a random digits table with conditional probability, what do you ALWAYS have to say?

You have to say no repeats.

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26

When simulating Independent events (allow/donā€™t allow) repeatsā€¦

allow

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27

When simulating conditional events, (allow/donā€™t allow) repeatsā€¦

donā€™t allow

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28

Whenever you are repeating a simulation given the probability of the same eventā€¦.

use exponents.

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