作者yuyhiyuy (y学姊)
看板NCCUPSYstudy
标题[考题] 962基础数学期中考
时间Thu Apr 17 23:00:14 2008
本次考试范围: 样本空间、条件机率、独立事件、贝式定理
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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