Q1:Suppose X and Y are independent events with marginal probabilities of 0.47 and 0.87 respectively.What is the probability that either event occurs?( 3 decimal places ) Q2：A Melbourne real estate agent lists two houses for lease in the same street

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Q1:Suppose X and Y are independent events with marginal probabilities of 0.47 and 0.87 respectively.What is the probability that either event occurs?( 3 decimal places ) Q2：A Melbourne real estate agent lists two houses for lease in the same street
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Q1:Suppose X and Y are independent events with marginal probabilities of 0.47 and 0.87 respectively.What is the probability that either event occurs?( 3 decimal places ) Q2：A Melbourne real estate agent lists two houses for lease in the same street
Q1:Suppose X and Y are independent events with marginal probabilities of 0.47 and 0.87 respectively.What is the probability that either event occurs?( 3 decimal places )
Q2：A Melbourne real estate agent lists two houses for lease in the same street,one built of brick and the other of timber.The agent estimates that the probability of being leased within one week is 0.69 for the brick and 0.68 for the timber house,and the probability of both being leased within one week is 0.52.If the timber house is leased within one week,what is the probability that the brick house is also leased within one week?Give your answer correct to three decimal places.

Q1:Suppose X and Y are independent events with marginal probabilities of 0.47 and 0.87 respectively.What is the probability that either event occurs?( 3 decimal places ) Q2：A Melbourne real estate agent lists two houses for lease in the same street
Q1：由题意,X、Y是相互独立的随机变量,并且各自发生的概率（即题目中说的边缘分布）分别为Px=0.47,Py=0.87.
题目要问的是“两者至少有一个发生的概率”,即事件A并（即符号U,百度不能打数学符号）B
由概率的加法公式（概率的一个性质）
P（A并B）＝P（A）+P(B)-P(A交B）
由于A、B是相互独立的随机变量,故P(A交B)＝P(A)P(B)=0.47*0.87＝0.4089
代入前式得
P（A并B）＝P（A）+P(B)-P(A交B）=0.47+0.87-0.4089=0.9311约等于0.931 完毕
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Q2：一个墨尔本房地产代理商列出了同一条街道上的两幢待出租的房子,一个是砖房,另一个是木房.代理商估计砖房在一个星期内能租出去的概率是0.69,而木房在一个星期内租出去的概率是0.68,而砖房和木房在一周内同时租出去的概率是0.52.问：如果木房在一个星期内租出,那么砖房在一个星期内也租出去的概率是多少?给出你的答案并保留结果至小数点后3位.
设A表示事件“砖房在一个星期内能租出去”,则P(A)＝0.69,设B表示事件“木房在一个星期内租出去”,则P(B)=0.68.那么A交B就表示“砖房和木房在一个星期内同时租出”,即P(A交B)=P(AB)=0.52.下面看问题要我们求什么.
“如果木房在一个星期内租出,那么砖房在一个星期内也租出去的概率是多少”,显然,这是条件概率问题.问题所求即为P(A|B).至此,对题目已经完全明白,并且建立合适的模型,接下来开始计算.
由条件概率公式
P(A|B)=P(AB)/P(B)
式子右边的分子和分母题目恰好都告诉我们了,代入得
P(A|B)=P(AB)/P(B)=0.52/0.68约等于0.765
（这里题目有了多余的条件P(A)＝0.69）
总结：主要是要把题目所讲的事件用数学语言描述,然后根据问题找出相应的数学模型（或者叫数学公式）去解决它.

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