Review Exam 2 (Chapter 13-18)/Math 1680/Ms. Stonebraker

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Review Exam 2 (Chapter 13-18)/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

      • P(not A) = 1 – P(A)

    • 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:

    • EVBOX is the average of a box model


    • SDBOX = (BIG – SMALL)

    • SE = SDSUM = SDBOX

    • Recognize that the sum is likely to be around the EVSUM 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


There is an additional question and answer time on Tuesday night April 12th t from 7-9pm in GAB 312. Make good use of this time. I will be there regardless if eighty people come or none shows.

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