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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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