SAMPLE College Math
Chapter 4: Counting and Probability
Overview
We make use of counting and probability in our everyday life very often, like when we say thereisa likelihood of rain tomorrow. Similarly,weoftenmakeuseofwordslikelikely,probably,chance,etc.In such cases, we are not certain about the future happening but we are certain that it will happen. Countingandprobabilityhelpequipyouwiththebasicunderstandingofdeterminingchanceswhenwe deal withdifferentexperiments,likethelottery,winningatcasinos,playingcards,andotherforecasts. Finally, it facilitates healthy decision making in the light of uncertain future in different disciplines. In this chapter, you will learn the concepts and application of different counting techniques and probabilitysituations.Thechapterwillmajorlycoverthefundamentalcountingprinciple,permutations, combinations, and theories of probability. The theories and techniques presented in this chapter will also be applied in real life situations by way of different arbitrary examples. Objectives
By the end of this chapter, you will learn, solve and gain expertise in:
● Counting technique and rule ● Permutation and combination ● Probability with mutually exclusive and independent events ● Union and intersection of probabilities ● Expected value of payoffs ● Conditional probability A. Counting
Mathematicsinvolvestheuseofcountingandwemakeuseofdifferentcountingthroughoutourday.For instance,yougotoCocoberryFrozenYogurt,whereyoucanselectaflavorandtoppingsforyourself.The vendor asks you to choose between green apple, mango, strawberry, blackberry, blueberry, or black currantasyourbaseflavor.Notjustthis,nowyouhavetochooseonetoppingamongthe12optionsof fruits, nuts, and syrups; in this example counting can help to determine the total number of ways in which you can select your flavor. Similarly,wemakeuseofcountingineverysphereoflife.Itiseasytodetermineinsimplecaseswhere the options available are less, for instance, travelling between two cities involves three ways. The problem arises when the number of choices increases, like the case of Cocoberry Frozen Yogurt. Let use learn some simple rules of counting that helps to solve suchproblems.Beforemovingtothe rules, let us solve one simple problem of counting.
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