1) Bag A contains 3 red balls and 2 yellow balls
Bag B contains 4 red and 5 yellow balls
A ball is drawn at random from A and placed in B
subsequently, a ball is drawn at random from B and placed in A
a) what is the chance that if the ball is now drawn from A it will be red?
ans: 143/250
b) if this ball is in fact red. what is the probability that the first two balls drawn are also red?
ans: 45/143
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2) A man chooses a painting at random from a group containing 8 originals and 2 copies.
He consults an expert whose probability of judging either an original or a copy correctly is 5/6.
a) if the expert considers that the chosen painting is an original, what is the probability that this is really so? ANS: 20/21
b) if the experts considers that the painting is a copy and the man returns it and chooses another painting at random from the other nine, what is the probability that this second painting is original?
ANS: 68/81
thanks
PROBABILITY !!! HELP! [20]
2011-09-29 8:22 pm
回答 (2)
2011-09-29 9:40 pm
✔ 最佳答案
1(a) P(3 rd draw from urn A is red)= P(A red, B red, A red) + P(A red, B yellow, A red) + P(A yellow, B red, A red) + P(A yellow, B yellow, A red)= (3/5)(5/10)(3/5) + (3/5)(5/10)(2/5) + (2/5)(4/10)(4/5) + (2/5)(6/10)(3/5)= 143/250(b) (3/5)(5/10)(3/5)/(143/250)= 45/1432(a) (5/6)(8/10)/[(5/6)(8/10) + (1/6)(2/10)] = 20/21(b) If the expert is right, then P(second painting is original) = 8/9If the expert is wrong, then P(second painting is original) = 7/9The probability that the expert is right = (5/6)(2/10)/[(5/6)(2/10) + (1/6)(8/10)] = 5/9So, the probability is (5/9)(8/9) + [(5/6)(2/10) + (4/9)(7/9)= 68/81 
收錄日期: 2021-04-23 23:23:58
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https://hk.answers.yahoo.com/question/index?qid=20110929000051KK00419