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SBM Chapter 7 Probability: Living with the Odds.

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SBM Chapter 7 Probability: Living with the Odds.

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    1. SBM Chapter 7 Probability: “Living with the Odds.” 7E: “Counting and Probability” A Brief Review: Factorials

    3. Factorials... Whenever a positive integer n is multiplied by all the preceding positive integers, the result is called n factorial and is denoted by the symbol n! This is read as “n factorial” 1! = 1 2! = 2 X 1 = 2 3! = 3 X 2 X 1 = 6 4! = 4 X 3 X 2 X 1 = 24 etc…

    4. Example One... Calculate the following?

    5. Example Two... A brand of ballpoint pen comes in five colors, with fine or regular point, and with standard, deluxe, or executive styling. How many different versions does the pen come in?

    6. Example Three... A seven-character computer password can be any three letters of the alphabet, followed by two numerical digits, followed by two more letters. How many different passwords are possible?

    7. Permutations... Mathematically, we are dealing with permutations whenever all selections come from a single group of items. no item may be selected more than once. the order of arrangement matters. The total number of permutations possible with a group of n items is n! where n! = n X (n X 1) X … X 2 X 1

    8. The Permutations Formula... If we make r selections from a group of n items, the number of permutations is: where is read as “the number of permutations of n items taken r at at time.”

    9. Example Four... From a normal deck of 52 playing cards, three cards are drawn and placed face up on a table, left to right. How many possible results are there of this procedure?

    10. Example Five... Ten finalists in a talent show must give final performances. Five contestants will perform on the first night of the show. How many different ways can the schedule for the first night be made?

    11. Combinations... Mathematically, we are dealing with combinations whenever all selections come from a single group of items. no item may be selected more than once the order of arrangement does not matter For example, ABCD is considered the same as DCBA.

    12. The Combinations Formula... If we make r selections from a group of n items, the number of possible combinations is: where is read “the number of combinations of n items taken r at a time.”

    13. Example Six... How many different ways are there to order a medium two-topping pizza, given that there are nine toppings to choose from?

    14. Example Seven... A scholar is choosing six books to take on vacation, from a stack of 34. How many different combinations of books are there?

    15. Probability & Coincidence... Coincidences are bound to happen. Although a particular outcome may be highly unlikely, some similar outcomes may be extremely likely or even certain to occur. In general, this means that coincidences will inevitably be experienced by someone, even if these coincidences have a low probability for any particular reason.

    16. Homework 7E: Part I #’s 1, 3 - 14 Part II #’s 15 - 20a, 22a, 22c, 23 - 29, 31, 33

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