7/28/2019 LPP + Probability
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ll. Kellogg is a new cereal ormed of a mixture of bran and rice,
that containsat least 88gramsof protein and at least 36 milligrams
of iron. Knou'ing that bran contains80gramsof protein and 40
milligrams of iron per kilogram, and that rice contains 100gramsof
protein and -'i0milligrams of iron per kilogram, find the minimum
cost ofproducing his new cereal l'bran costsRs.5 per kilogram and
rice costs Rs.4 perkilogram.A dealer wishes to purchasea number of
fans and sewing machines.He has onlyRs.5760o investand hasspace or
at most 120 tems.A fan costshim Rs.360and asewingmachineRs.240.
I:[e expects o sell a fan at a profit of Rs.22 and a
sewingmachineat aprofit of Rs.I8. Assuming hat he cansell all the
items hat he buys, howshould he invest his morrey o maximize the
profit? Solve graphically and find themaximumprofit.Anil wants o
investat the most Rs.12000n bondsA and B. According o rules,hehas o
investat leastRE.2000n bond A andat leastRs.4000n BondB. If the
rate ofinterestof bondA is 8'loper annumand on Bond B, it is l\Yo
per annum,how shouldhe investhis moneyfor maxirrum interest?Solve
he problemgraphically.A factoryhas hreemachines,X, Y andZ,
producing1000,2000 and3000 boltsperdayrespectively. he machineX
produceso/odefective olts,Y
produces.5YoandZproduces2o/odefectivebolts. At the end of the
day,abolt is drawn at randomand t isfound to be defective. V'hat is
the probability that this defective bolt has beenproducedby the
machine .1?In a bolt factory, hreemrrchinesA, B, C
manufacture25yo,35Yoand40Yoof the totalproductionrespectively.Of
their respectiveoutputs,5o/o, Yoand2Yoaredefective.Abolt is drawn
at randonr rom the total productand t is found to be defective.Find
theprobabilitythat it was rnanufactured y themachineC.An
insurancecompany nsured2000 scooterdrivers,4000 car drivers and6000
truckdrivers. The probability of ar": ccident nvolving a scooter,a
car anda truck is l/100,31100and3120 espectively.One of the
insuredpersonsmeetswith an accident.Whatis theprobabilitythat he is
a scoterdriver.A doctor is to visit a patient.From pastexperience,t
is known that the probabilitiesthat he will comeby train,
bus,scooteror by car are espectively /10, ll5, lll0 and2/5.
Theprobabilities hat I'rewill be ate ue Yo, l3 and /12, if he
comesby train,busand scooter espective$f blt if he comesby car,he
will not be late. When he arrives,he s late.What is the$robability
that he hascomeby train?8. In an examination, n
exanftrpeeitherguessesr copiesor knows he answero a
3.
4.
5.
6.
7.
choices.The probability that he makesa guess s(1i3) and the
probability thatJhecopies he answer s (l/6). The probability har
hisanswer s correct,given that the copied t, is (1/8). The
probability that his answer scorrect,giventhat he guesseilt, is
(1/4). Find the probability that he knew the answerto the
question,giventhat he;correctlyansweredt.9. Urn A contains white,
2hIack and 3 red balls;urn B contains2 white,lblack and Ired ball;
and urn C contains4 white, 5 black and 3 red balls. One urn is
chosenatrandomand two balls are ,Jrawn.Thesehappen o be one white
and onered. What istheprobabilitythat they crme from urn A?10.A
card from a pack of 52 cafis is lost. From the remaining cardsof
the pack, twocardsare drawn and are found to be both spades. ind
the probability of the lost cardbeinga spade.
In an examination,an exanf{neeeithermultiple-choicequestionwitt{
four cho:(1i3) and the probability thatJhecopier
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