GCNU311A_Lecturer.docx - ITE3706/ITE3707 Foundation Mathematics II(A/II(B GCNU311A – Notes Unit Title Solve problems involving uncertainty 不確定�

GCNU311A_Lecturer.docx - ITE3706/ITE3707 Foundation...

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ITE3706/ITE3707 Foundation Mathematics II(A)/II(B) GCNU311A – Notes Unit Title Solve problems involving uncertainty 不確定性 using basic principles of probability 概率 Unit Code GCNU311A Warmup with Gamification “Tong Pak Fu and Chou Heung – The Probabilistic Fantasy ( 唐伯虎點秋香 – 概率幻想 )” Chapter 1: The First Sight ( 第一幕:邂逅 ) 1. Definition of Probability 概率 / 機率 / 機會率 / 或然率 The probability ( P ) that an event that may happen is given by: Probabilityof an event = P ( event )= Number of Favourable Outcomes 合適的結果 Total Number of Possible Outcomes 可能的結果 In order to use this formula, we need to be able to count the number of outcomes correctly . From the formula, we can realise some basic properties of probability: 0 ≤P ( event ) 1 Probability 0 means an event that will never happen Probability 1 means an event that is certain to happen 1.1. Empirical Probability 實驗概率 If the number of favourable outcomes is collected from observations during an experiment, the probability calculated is called empirical (or experimental) probability. 1.2. Theoretical Probability 理論概率 With theoretical probability, we would not actually conduct an experiment. Based upon knowledge of the situation, we arrive at the “expected 預 期 的 ” answer of the number of favourable outcomes to the number of possible outcomes. 2. Method of Counting We use the curly brackets { } to enclose the outcomes. The possible outcomes of tossing/throwing/rolling a die 一顆骰子 are { 1, 2, 3, 4, 5, 6 } . The possible outcomes of flipping/tossing a coin 一枚硬幣 are { H, T } , that is head or tail . p. 1 of 19
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ITE3706/ITE3707 Foundation Mathematics II(A)/II(B) GCNU311A – Notes Example 1. Consider flipping of a fair 公平的 coin twice and we want to have one head only . (a) List all the possible outcomes and find the number of outcomes. (b) List all the favourable outcomes and find the number of outcomes. (c) Find the probability of getting one head only. Solution: (a) Possible outcomes are { HH, HT, TH, TT } The total number of possible outcomes is 4. (b) As we are only interested in having one head, favourable outcomes are { HT, TH } The number of favourable outcomes is 2. (c) P ( only oneheadby tossing acointwice )= 2 4 = 1 2 = 0.5 The probability of getting only one head is 0.5. Example 2. Consider tossing of a fair die. (a) What is the probability of obtaining an even number? (b) Find the probability of getting an odd number. (c) Calculate the probability of getting the number “ 6 ”. (d) Determine the probability of getting a number smaller than 3 . Solution: (a) Possible outcomes are { , , , , , } The total number of possible outcomes is 6. As we want to find out the probability of getting an even number, so the favourable outcomes are { , , } The number of favourable outcomes is 3.
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