同感，答案有问题。楼主对。

如果这个题在这里是“但他的味道检测对于劣质车则有2/3的失误.”即：他对于劣质车有2/3的概率检测为好车。

此题应该用贝业斯公式来算

再设C为“一辆车是坏车”

P(B|A)=P(A|B)P(B) / P(A|B)P(B) +P(A|C)P(C) =1*1/2 / 1*1/2+2/3*1/2=3/5

然后再按这个概率计算期望1000*(3/5)+100*(2/5)=640

楼主需明确的是你的P(AB)和P(A)各代表着什么

P(AB)意味着事件A,B同时发生的概率，不妨再由条件概率定义，P(AB)=P(A|B)P(B)=1*1/2

而P(A)则是通过检测的概率，由全概率公式有，P(A)=P(A|B)P(B) +P(A|C)P(C)，其中C为劣质车的事件

其中只需注意的是，P(A|C)即劣质车通过检测确认其为劣质车的概率，2/3

通过检测是指检测成功，并不是指确定其为优质车

Rod's Auction House in Bent Crankshaft, Oregon, holds sealedbid used-car auctions every Tuesday. Each used car is sold to the highest bidder at the second-highest bidder's bid. On average, half of the cars that are sold at Rod's Auction House are lemons and half are good used cars. A good used car is worth $1,000 to any buyer and a lemon is worth only $100 to any buyer. Buyers are allowed to look over the used cars for a few minutes before they are auctioned. Almost all of the buyers who attend the auctions can do no better than random choice at picking good cars from among the lemons. The only exception is Al Crankcase. Al can sometimes, but not always, detect a lemon by licking the oil o of the dipstick. A good car will never fail Al's taste test, but 1/3 of the lemons fail his test. Al attends every auction, licks every dipstick, and taking into account the results of his taste test, bids his expected value for every car.

How much will Al bid for a car that passes his taste test?

谢谢上面几位的回复. 把原题目帖上.看来这个题目主要问题在于意思的理解. 看来我理解错了,题目说劣质车有1/3不能通过检测,其实意思应该是有2/3的劣质车会通过检测而被认为是好车. 所以3楼的解法应该是正确的.