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Shadi G.

Margin of Error

1 / square root of n

95% confidence interval

- Subtracting and adding the margin of error from the sample proportion.
- You can be 96% confident that the true population proportion lies within this interval

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Outcomes

The most basic possible results of observations or experiments

Event

One or more outcomes that share a property of interest

Probability of an Event

Always between 0 and 1

- probability of 0 means that the event in impossible
- probability of 1 means the event is certain

Theoretical Probability

- It is based on a model in which all outcomes are equally likely
- it is determined by dividing the number of ways an event can occur by the total number of possible outcomes

Empirical Probability

- It is based on observations or experiments
- it is the relative frequency of the event of interest

Probability of an Event Not Occurring

1 - P(A)

And Probability: independent events

- independent if the outcome of one event doesn't affect the probability of the other event
- P(A and B) = P(A) x P(B)

And Probability: dependent events

- dependent if the outcome of one event affects the probability of the other event
- P(A and B) = P(A) x P(B given A)

Either/Or Probability: non-overlapping events

- non-overlapping if they cannot occur together
- P(A or B) = P(A) + P(B)

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Either/Or Probability: overlapping events

- overlapping if they can occur together
- P(A or B) = P(A) + P(B) - P(A-B)

The Law of Large Numbers

Larger number of trials will lead to the event's proportion getting closer and closer to probability P(A)

Expected Value

EV= (event 1 value) x (event 1 probability) + (event 2 value) x (event 2 probability)

Gambler's Fallacy

the mistaken belief that a streak of bad luck makes a person "due" for a streak of good luck

Arrangements with Repetition

If we make r selections from a group of n choices, a total of n x n x n x n....n(^r)

Permutation

- Order does matter
- nPr = n!/(n-r)!

Combination

- Order does not matter
- nCr = n!/(n-r)r!

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