procrastination is a rampant disease that affects approximat

来源：学生作业帮编辑：拍题作业网作业帮分类：英语作业时间：2024/05/07 13:09:46

procrastination is a rampant disease that affects approximately 80% of students in canada.a test to screen for procrastion will show a positive result 90% of the time if the students actually suffers from the ailment.but there is a 5% chance of a false positive.
a) what is the probability that the test will give a correct result.0.91 但我不知道怎么得出来的
b) if you test positive for procrastination,what is the probabilyty that you actually suffer from the disease?
这是关于一个疾病
那不是什么托拉疾病
而且也不是什么恶习的
但还是麻烦你们了

我翻译的时候是意译的.疾病是一个比喻的说法.说拖延这种习惯就像疾病一样传播.本来这道题是在中文概率书上以癌症检测的形式出现的.现在包装成这样,能让学生觉得更有趣一些.
你可以用金山词霸.我研究生英语免修,你相不相信我随意
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大概意思是这样的：
拖延（拖拉）这种恶习像疾病一样.假设大约80%的加拿大学生有拖延习惯.而一种判断某学生是否拖延的测试,对于确实有拖延恶习的学生,90%可能会判断正确.但是对于没有拖延习惯的学生,也有5%的可能会判断拖延.
a)这个判断测试的正确率是多少?
b)如果这个测试判断你是拖延的,那么你真的有拖延习惯的概率是多少?
解法：
把所有情况分为4种分别计算概率
学生拖延,判断拖延：0.8 * 0.9 = 0.72
学生不拖延,判断拖延：0.2 *0.05 = 0.01
学生拖延,判断不拖延：0.8*0.1 = 0.08
学生不拖延,判断不拖延：0.2*0.95 = 0.19
a)判断正确的情况就是：
拖延被判拖延+不拖延被判不拖延
= 0.72 + 0.19 = 0.91
b)已知判断你是拖延的,
那么有两种情况：
你实际拖延的概率 0.72
你实际不拖延的概率 0.01
那么你真有拖延的概率
= 0.72/(0.72+0.01) = 0.98
你也可以用全概率公式和贝叶斯公式来做

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