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.‬

‭© 2023 ACHIEVE ULTIMATE CREDIT-BY-EXAM GUIDE‬‭|‬‭COLLEGE MATH‬

‭53‬

Made with FlippingBook - Online Brochure Maker