29.An insurance company has a paper record and an electronic record for every claim. For an inaccurate paper record, 60% chances that the electronic record is inaccurate. For an inaccurate electronic record, 75% chances that the paper record is inaccurate. 3% of all the claims are inaccurate both in paper record and in electronic record. Pick one claim randomly, what are the chances that it is both accurate in paper record and in electronic record?
A.97% B.94% C.68% D.65% E.35%
【确定】B 94%,
思路：考条件概率，p(B|A)=60% p(A|B)=75%.p(AB)=3%, 1-p(A+B)=94%
For an inaccurate paper record, 60% chances that the electronic record is inaccurate.
x * 60% = 3% x = 5% (inaccurate paper record)
For an inaccurate electronic record, 75% chances that the paper record is inaccurate.
y * 75% = 3% y = 4% (inaccurate electronic record)
=> 2% inaccurate paper record, accurate electronic record
=> 1% inaccurate electronic record, accurate paper record
inaccurate paper record + inaccurate electronic record = 6%
ans:94%
简单地说，就是：
设X个inaccurate paper record，
设Y个inaccurate electronic record
总CLAIMS 是I，则
X*60% = 3%*I， x = 5% *I
y * 75% = 3%*I， y = 4% *I
由于两者的交集是3% *I，所以真正的不合格的为5+4-3=6% * I
任选一个是错误的，6%*I/I =6%
因此，选一个是没错误的，就是94%
