Probability

Question 1

Probability

Answer 1

number of ways to get desired outcome / total possible outcomes

Question 2

Compound Events

Answer 2

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

Question 3

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

Answer 3

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

Question 4

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

Answer 4

n! / (n-x)!x!

Question 5

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

Answer 5

5! 5x4x3x2x1

Question 6

Look for permutations anytime order…

Answer 6

matters

Question 7

Look for combinations anytime order…

Answer 7

does not matter

Question 8

Enumeration

Answer 8

writing it out

Question 9

Factorial

Answer 9

n! n x n-1 x n-2…

Question 10

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

Answer 10

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

Question 11

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

Answer 11

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

Question 12

Complement (of any event, A)

Answer 12

The probability of A not happening

Question 13

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

Answer 13

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

Question 14

Joint Probability

Answer 14

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

Question 15

Independent events

Answer 15

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

Question 16

Mutually exclusive events

Answer 16

Cannot happen at the same time

Question 17

Conditional probability

Answer 17

Event A happening depends on if B happens

Question 18

Normal distribution model

Answer 18

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

Question 19

Z-score (standard value)

Answer 19

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

Question 20

Normal Model / Bell Shaped curve %’s

Answer 20

68% w/in 1 st dv

95% w/in 2 st dv

99.7% w/in 3 st dv

Question 21

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

Answer 21

data

Question 22

what does a Z-Score do?

Answer 22

compares things in totally different groups (apples to oranges)

Question 23

Higher Z-Score compared to lower Z-Score

Answer 23

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

Question 24

Z-Score equation

Answer 24

Z = (y-y’)/st dev or diff/st dev

Question 25

What is Expected Value?

Answer 25

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

Question 26

Variance

Answer 26

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

Question 27

How do you calculate the variance?

Answer 27

sum of variances/number of instances

Question 28

Shows 5 stats: Min Score, Max Score, and three percentiles

Question 29

What is population?

Answer 29

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

Question 30

What is a Sample?

Answer 30

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

Question 31

What is a survey?

Answer 31

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

Question 32

Simple Random Sampling (SRS)

Answer 32

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

Question 33

What is Linear Regression?

Answer 33

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.

Question 34

What are the linear regression variables?

Answer 34

y = dependent variable x = independent variable

Question 35

What is a Chi-Squared value?

Answer 35

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.

Question 36

How do you calculate the Chi-Squared value?

Answer 36

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

Question 37

What is the **R** coefficient?

Answer 37

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