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本次考試範圍: 樣本空間、條件機率、獨立事件、貝式定理 I.SAMPLE SPACES Determine the sample spaces of the following random experiments: (i)The experiment of tossing a coin three times. (ii)The experiment of tossing a coin two times and a dice. (iii)The experiment of drawing two balls numbered 1~n from an urn with/without replacement. II.CONDITIONAL PROBABILITY (i)Given two urns, suppose urn 1 contains four black and seven white balls, and urn 2 three black, one white, and four yellow. We select an urn at random and then draw a ball. What is the probability that we obtain a balck ball? (ii)Data collected by the Office of Admissions indicate the following choices made by the students of the freshman clas regarding their majors: Major Percentage of Freshmen Chossing Major Female(in%) Male(in%) Engineering 26 40 60 Business 30 35 65 Education 9 80 20 Social science 12 52 48 Natural science 12 56 44 Humanities 9 65 35 Other 2 51 49 What is the probability that female student selected at random from the freshman class in majoring in engineering? III.INDEPENDENT EVENT? Decide whether the following wvwnts are independent (i)For a 3-child family let E be the event "The family has at most 1 boy" and let F be the event "The family has children of wach sex". (ii)A fair coin is tossed twice. Let E the event "A head turns up on the first throw" and let F be the event "A tail turns up on the second throw". IV.THE VAYES FORMULA (i)Formulate the Bayes Formulate. (ii)In a human population 51 percent are male and 49 percent are female. 5 percent of male and 0.3 percent of the female are color-blind. If a person is randomly chosen from the population is found to be color-blind, what is the probability that the person is a male? --



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