Review Exam 2 (Chapter 1318)/Math 1680/Ms. Stonebraker
Study: Quizzes, notes, and reread through the book starting with the summary portion of the chapters. If you have time, work through problems in the book again…
Chapter 13 (What are the Chances?) / Chapter 14 (More about Chances):

Be able to:

Make use of the multiplication rule

Make use of the addition rule

Recognize, discuss, and justify independence and dependence

Find the probability there is at least one __________

Find the probability there is no __________

Make use of compliments

Recognize a scenario’s sample space and sample size

For Example: Roulette has a sample size of 38, and its sample space is 0, 00, 1, …, 37, and 38.

Quizzes are a great study guide for this and pretty much all of the sections.
Chapter 15 (Binomial Formula):

Be able to:

Recognize when you can and cannot use binomial formula

To use binomial

Each time the process is repeated, outcomes can be classified as either successes or failures

Each time the process is repeated there is the same probability of a success occurring

Successive outcomes are independent of one another


Recognize when you need to use combination and when you need to use permutation

Simplify permutations or combinations

nCr = = …order doesn’t matter

nPr = ….order is significant

Work a problem applying the binomial formula when we are trying to find the probability of having

Exactly a certain amount of successes

More than a certain amount of successes

Less than a certain amount of successes

At least a certain amount of successes

No more than a certain amount of successes
Chapter 16 (The Law of Averages):

Be able to:

Apply the law of averages

Recognize when the law of averages is in favor of a certain event or not

Find absolute chance error and relative chance error given a scenario

Set up a box model for an independent chance process

Recognize how many draw will be needed from the box
Chapter 17 (The Expected Value and Standard Error):
This section is important. Pay close attention and be able to work out what lies within.

Be able to:

EV_{BOX} is the average of a box model

EV_{SUM }= EV_{BOX } N

SD_{BOX} = (BIG – SMALL)

SE = SD_{SUM} = SD_{BOX}

Recognize that the sum is likely to be around the EV_{SUM} give or take the SE or so.

Use these values to standardize a sum

Use the normal chart to determine the probability that your sum is less than, more than, or between certain values.

Remember when you can and cannot use normal approximation

You have to use binomial if the number of draws are less than 30

Use a box model to evaluate the sum of draws to find

Net Gain/loss

This answers the question “how much…?”

You use the amount you win and lose to construct the box model

Count the number of times an event occurred

This answers the question “how many …?”

You use 0’s and 1’s to construct this model
Chapter 18 (The Normal Approximation for Probability Histograms):

Be able to:

Read a histogram and discuss how the bars represent probabilities

Discuss and apply the central limit theorem

Discuss what an empirical histogram is and when it starts to follow the expected probability histogram
Remember:
There is an additional question and answer time on Tuesday night April 12^{th} ^{t} from 79pm in GAB 312. Make good use of this time. I will be there regardless if eighty people come or none shows.
