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Ebook Certificate Paper C3 - Fundamentals of business mathematics: Part 2

Ebook Certificate Paper C3 - Fundamentals of business mathematics: Part 2 presents the following content: Probability; Financial mathematics; Inter-relationships between variables; Forecasting; Spreadsheets. Please refer to the documentation for more details. | Part C Probability 165 166 Probability Introduction The likelihood of rain this afternoon is fifty percent warns the weather report from your radio alarm clock. There s no chance of you catching that bus grunts the helpful soul as you puff up the hill. The headline on your newspaper screams Odds of Rainbow Party winning the election rise to one in four . Likelihood and chance are expressions used in our everyday lives to denote a level of uncertainty. Probability is the mathematical term used when we need to calculate the likelihood of an event happening. This chapter will therefore explain various techniques for assessing probability and look at how it can be applied in business decision making. Topic list Syllabus references 1 The concept of probability B i 1 2 The rules of probability B ii iii 2 3 3 Expected values B iv 4 4 Expectation and decision making B v vi vii 4 5 167 1 The concept of probability 1.1 Introducing probability FAST FORWARD Probability is a measure of likelihood and can be stated as a percentage a ratio or more usually as a number from 0 to 1. Consider the following. Probability 0 impossibility Probability 1 certainty Probability 1 2 a 50 chance of something happening Probability 1 4 a 1 in 4 chance of something happening 1.2 Expressing probabilities In statistics probabilities are more commonly expressed as proportions than as percentages. Consider the following possible outcomes. Probability as a Probability as Possible outcome percentage a proportion A 15.0 0.150 B 20.0 0.200 C 32.5 0.325 D 7.5 0.075 E 12.5 0.125 F 12.5 0.125 100.0 1.000 It is useful to consider how probability can be quantified. A businessman might estimate that if the selling price of a product is raised by 20p there would be a 90 probability that demand would fall by 30 but how would he have reached his estimate of 90 probability 1.3 Assessing probabilities There are several ways of assessing probabilities. They may be measurable with mathematical certainty If a coin is