College Math

College Math Study Guide

Chapter 4: Counting and Probability Overview We make use of counting and probability in our everyday life very often, like when we say there is a likelihood of rain tomorrow. Similarly, we often make use of words like likely, probably, chance, etc. In such cases, we are not certain about the future happening but we are certain that it will happen. Counting and probability help equip you with the basic understanding of determining chances when we deal with different experiments, like the lottery, winning at casinos, playing cards, and other forecasts. 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 probability situations. The chapter will majorly cover the fundamental counting principle, 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 4.1 Counting Mathematics involves the use of counting and we make use of different counting throughout our day. For instance, you go to Cocoberry Frozen Yogurt, where you can select a flavor and toppings for yourself. The vendor asks you to choose between green apple, mango, strawberry, blackberry, blueberry, or black currant as your base flavor. Not just this, now you have to choose one topping among the 12 options of 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, we make use of counting in every sphere of life. It is easy to determine in simple cases where 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 .

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