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Probability - Difficulty level 700+

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Intern
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Joined: 07 Jul 2010
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WE 1: 5 years
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Probability - Difficulty level 700+ [#permalink] New post 19 Jun 2012, 14:32
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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?
Intern
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Status: ISB 14...:)
Joined: 25 May 2012
Posts: 30
Location: India
Concentration: Strategy
Schools: ISB '14 (A)
GMAT 1: 750 Q51 V39
GPA: 3.62
WE: Engineering (Energy and Utilities)
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Kudos [?]: 22 [0], given: 10

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Re: Probability - Difficulty level 700+ [#permalink] New post 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

Solving the above equation,

p< 4/7

Someone else will answer II...:D
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Re: Probability - Difficulty level 700+ [#permalink] New post 20 Jun 2012, 00:05
Thank you for the solution.... I am not sure if that is right bc i don't have the answer.

you solved the question applying logic for statistically independent events...

I understand that P(AB)= P(A)*P(B)

where A - is WTR research
and B - is investigation

A and B are independent events but awarding contract to Litre is dependent event, that depends upon 2 independent events thats A and B

and for dependent events logic is P(XY)/P(Y)

where Y is the probability of A and B
and X is litre's being awarded contract.

this question was given to us in GMAT preparation class as practice test....
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Re: Probability - Difficulty level 700+ [#permalink] New post 25 Jun 2012, 07:25
Nice practice question but why bother with questions that, in wording, length and other criteria, will probably never appear on the real test.
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+1 Kudos me - I'm half Irish, half Prussian.

Re: Probability - Difficulty level 700+   [#permalink] 25 Jun 2012, 07:25
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