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Probability - Difficulty level 700+ [#permalink]
19 Jun 2012, 14:32
Al Cascade ,president of the litre coporation is studying hiscompany's chances of being awarded an important water purificationsystem contract for the Tennessee Valley Authority.Accordingly twoevents are intrest to him.First ,litres major competitor,WTR isconducting purification research,which it hopes to complete beforecontract award deadline.Second,TWA is investigating all recentcontrcators, of which litres is one and WTR is not.If WTRfinishes its research and there is no investigation,then litresprobability of being awarded the contract is 0.67.If there is aninvestigation but WTR doesn't finish its research,the probabilityis 0.72.If both event occur , the probability is 0.58, if neitheroccurs,the probability is 0.85. The occurence of an investigationand WTR's completion of research in time are independentevents.
1.Suppose that AL knows that the probability of WTR'scompleting its research in time is 0.80.How low must theprobability of an investigation be so that the probability ofLitre's being awarded the contract is at least 0.65 ? 2.Suppose Al knows that the probability of an investigation is0.70.How low must the probability of WTR's completing its researchon time be so that the probability of litres being awarded thecontract is at least 0.65? Suppose that the probability of an investigation is 0.75 andthe probability of WTR's completiong its research in time is0.85.What is the probability of litre's being awarded thecontract?
Re: Probability - Difficulty level 700+ [#permalink]
19 Jun 2012, 18:37
I suppose this is not a Gmat kind of question.
1. Probability of research = 0.8 Probability of not completing research in time = 0.2 let 'p' be probability of an investigation
Probability of Litre being awarded contract depends on 4 possible cases and the probabilities of each case is given. Expressing the same mathematically, (0.8 * p * 0.58) + (0.8 * (1-p) * 0.67) + (0.2 * p * 0.72) + (0.2 * (1-p) * 0.85) > 0.65