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CSET Math II > Probability > Flashcards

Probability Flashcards

1
Q

Probability

A

number of ways to get desired outcome / total possible outcomes

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2
Q

Compound Events

A

a combination of simple events (ie: rolling two dice or flipping a coin three times)

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3
Q

Permutations: How many different ways can we arrange x items out of n in which order matters?

A

If no repetition is allowed, use: n! / (n-k)! If repetition is allowed, used: n^x

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4
Q

Combinations: How many ways are there to arrange x items out of n in which order does NOTmatter?

A

n! / (n-x)!x!

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5
Q

In how many unique orders can 5 horses finish a race? (hint: combination because order does not matter)

A

5! 5x4x3x2x1

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6
Q

Look for permutations anytime order…

A

matters

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7
Q

Look for combinations anytime order…

A

does not matter

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8
Q

Enumeration

A

writing it out

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9
Q

Factorial

A

n! n x n-1 x n-2…

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10
Q

Conditional Probability of disjoint independent events (ie: rolling an odd number or a 4 on one die)

A

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

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11
Q

Conditional Probability of non-disjoint independent events (ie: choosing a spade or a jack)

A

P(A or B) = P(A) + P(B) - P (A and B) subtract the overlap

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12
Q

Complement (of any event, A)

A

The probability of A not happening

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13
Q

If two events are DISJOInT ie: rolling an odd number or a 4 on one die?

A

Add the two events Ie: 1/2 + 1/6

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14
Q

Joint Probability

A

The probability of the intersection of two events (probability that both events occur)

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15
Q

Independent events

A

The probability of one is not affected by whether the other event occurred

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16
Q

Mutually exclusive events

A

Cannot happen at the same time

17
Q

Conditional probability

A

Event A happening depends on if B happens

18
Q

Normal distribution model

A

68% within +-1 standard deviations of the mean 95% within +-2 standard deviations of the mean 99.7% within +-3 standard deviations of the mean

19
Q

Z-score (standard value)

A

Way to compare an event y to the mean y^-

20
Q

Normal Model / Bell Shaped curve %’s

A

68% w/in 1 st dv

95% w/in 2 st dv

99.7% w/in 3 st dv

21
Q

The normal model is more bell shaped and symmetrical with more…

A

data

22
Q

what does a Z-Score do?

A

compares things in totally different groups (apples to oranges)

23
Q

Higher Z-Score compared to lower Z-Score

A

A Z-Score of 3 is VERY far above the mean, whereas a Z-Score of 0.2 is just above the mean

24
Q

Z-Score equation

A

Z = (y-y’)/st dev or diff/st dev

25
Q

What is Expected Value?

A

An estimate of the mean calculated by the weighted average of all possible values. Weights are the probabilities.

26
Q

Variance

A

a measure of dispersion - it tells us how far a set of values spread out from each other and how far each value is away from the mean

27
Q

How do you calculate the variance?

A

sum of variances/number of instances

28
Q

Shows 5 stats:

Min Score, Max Score, and three percentiles

A
29
Q

What is population?

A

Population is all items of interest, and has Parameters (ie: mean and standard deviation)

30
Q

What is a Sample?

A

A sample is a subset of the population, and has statitstics

31
Q

What is a survey?

A

A sampling of facts, figures, or opinions used to approximate something about a population. A good survey sample should be random and representative.

32
Q

Simple Random Sampling (SRS)

A

Every possible sample of n individuals is equally likely to be selected

33
Q

What is Linear Regression?

A

A facy name for the line of best fit

A techinique by which one dependent variable (y) is regressed againsted one independent variable (x), and the relationship between the two is in the form of a straight line.

34
Q

What are the linear regression variables?

A

y = dependent variable

x = independent variable

35
Q

What is a Chi-Squared value?

A

Looks at frequencies. Goodness of fit test. Do the values have a lot of deviation from the expected outcome? The null hypothesis is accepted or rejected.

36
Q

How do you calculate the Chi-Squared value?

A

The sum of (observed - expected)^2 over expected

37
Q

What is the R coefficient?

A

The correlation coefficient. Measures how close the data are to the fitted regression line. The closer to 1 (pos correlation) or -1 (neg correlation), the better the fit

CSET Math II (3 decks)

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