Applied MathematicsChap. 1 Probability & Probability Distribution M. Aamir Sir 900 40 5 1641 Chapter: 01 - 24 Marks 1 1.Probability Distribution 1.Binomial Distribution 6 Marks 1.An Unbiased coin is tossed 6 times. Find the probability of getting 2 heads. (2mks)W07/SQPg 2.An Unbiased coin is tossed 5 times. Find the probability of getting a head. (2mks)type W13/W09 3.An Unbiased coin is tossed 6 times. Find the probability of getting atleast 4 heads.( 2mks)W10,S11 4.A coin is tossed 3 times. Find the probability of getting exactly two tails. ( 2mks)S14 5.If two coins are tossed simultaneously, then find probability that at least one head appears.W12 6.A cubic die is thrown 4 times. What is the probability of obtaining at least one six.(2mks)Sqp 7.On an average 10% of the products manufactured by a certain machine are defective. If from these products four are chosen at random, find the probability that: i) 1 of them is defective.Ii) none iii) at most 2 bolts will be defectiveW07/SQPg 8.If 20% of the bolts produced by a machine are defective, then determine the probability that out of 4 bolts drawn, i) One is defective.At the most two are defective. / ii) not more than 1 is defective. ., S11, W12,W13 9.The probability that a bulb manufactured by a company will be defective is 110. If 12 such bulbs are manufactured, find the probability that i)Exactly 3 will be defective. ii)None will be defective. W10 10.10% of the components manufactured are defective. If 12 components are selected at random. Find the probability that at least 2 will be defective. S09/W10 11.On an average 310 electrical components in a packet are defective. If 4 items are selected at random and tested, what is the probability that not more than one is defective? 12.The probability that a man aged 65 will live to 75 is 0.65. What is the probability that out of 10 men which are now 65, 7 will live to 75?S14 13.Assuming that it is true that 2 in 10 industrial accidents are due to fatigue. Find the probability that exactly 2 of 8 industrial accidents will be due to fatigue. (2mks)S09/W08/S12 14.In 200 sets of Tosses of 5 fair coins in how many ways you can expect: i)At least two heads ii)At most two heads.S08 Formula to be used:1. =

.

. ()(For Binomial Distribution) Where: p = Normal probability of success. q = Normal probability of failure = 1-p. r = Questioned probability of success. n = Questioned total probability. 2. =

.!(For Poisson Distribution) At least= kam se kam, woh aur uske upar chalega. At most = zyada se zyada, woh aur uske niche chalega. Less than = Isse kam, (leaving this) iske niche chalega. More than = Isse zyada, (leaving this) iske upar chalega. Applied MathematicsChap. 1 Probability & Probability Distribution M. Aamir Sir 900 40 5 1641 Chapter: 01 - 24 Marks 2 2.Poisson Distribution 4 or 8marks1.If P (2) = P (3), Find P (5). (Given 3 = 20. )W10, S11 2.If 3% of the electric bulbs manufactured by a companyare defective, find the probability that in a sample of 100 bulbs: i) 5 bulbs are defective ii) At the most 2 bulbs will be defective.W12 S08/S12 3.If 2% of the electric bulbs manufactured by a companyare defective, find the probability that in a sample of 100 bulbs: i) 3 are defective ii) At least two are defective.S14 4.If the probability of bad reaction from a certain injection is 0.001, determine the change that out of 2000 individuals more than two will get a bad reaction (Given2 = 7.3891).W09, S11,SQPg,S14 5.Assumingthatprobabilityofafatalaccidentinafactoryduringtheyearis 11200.Calculatethe probability that in a factory employing 300 workers, therewill beatleast two fatal accidents in a year given that 0.25 = 0.7788.W07 6.Thenumber ofroadaccidents metwithbytaxidriversfollowsPoissondistributionwith mean2. Out of 5000 taxis in the city, find the number of drivers: i)Who do not meet with an accident? ii)Who met with an accident more than 3 times? Given2 = 0.8564.W08 7.Afirmproducesarticlesofwhich0.1percentisdefective,outof500articles.Ifwholesaler purchases 100 such cases, how many can be expected to have 1 defective? (0.5 = 0.6065).S09 8.Using Poissons distributions find the probability that the ace of spades will be drawn from a pack of well shuffled cards at least once in 104 consecutive trials. W13 /Sqp 9.Fit a Poisson distribution to the set of observations.(Given3 = 0.04974)SQPg X01234 F3082649286 3.Normal Distribution-1.Sacksofsugarpackedbyanautomaticloaderhaveanaverageweightof100kgwithstandard deviation0.250kg.Assumingnormaldistribution,findthechanceofsackyet weightinglessthan 99.5kg. (S.N.V. area z=0 to z=2 is 0.4772).S09 2.In a certain exam 500 students appeared. Mean score is 68 with S.D. 8. Find the no. of students: i)Scoring Less than 50.ii) Scoring more than 60S08/W10 (Given that area between Z = 0 to Z = 2.25 is 0.4878 and area between Z = 0 and Z = 1 is 0.3413) 3.The mean intelligence level of a group of children is 60 with a S.D. of 20. Assuming that intelligence level is normally distributed. Find the percentage of children with intelligence level over 100. (Given area between z = 0 to z = 0.5 is 0.1915, Z2=0.4772) Sqp/S12 4.In a sample of 1000 students the mean of a certain test is 14 and S.D. is 2.5 assuming distribution to be normal. Find how many score: i) between 12 and 15 ii) above 18. (Given A(0.8) = 0.2881, A(0.4) = 0.1554 and A(1.6) = 0.4452)SQPg,W13 5.Afactorymanufactured2000electricbulbswithaveragelifeof2040hoursandstandardof60 hours.Assumingnormaldistributionfindthenumberofbulbshavinglife: a)Between1920hours and 2160 hours b) more than 2150 hours. Given the area Z0 to Z = 1.83 is 0.4667, Z2=0.4772) S11 6.A sample of 1000 bulbs is distributed normally with mean life1620 hrs and S.D. 300 hrs. Find the number of bulbs which would die out after useful life of 900 hrs. (Area Z=2 .4 is 0.4918)W08 Applied MathematicsChap. 1 Probability & Probability Distribution M. Aamir Sir 900 40 5 1641 Chapter: 01 - 24 Marks 3 2.Probability 1.Basic Probability and Choosing (Drawing)- 2 & 8 Marks1.Find a probability of getting atleast a head if coin is tossed twice.2mk SQP/W10 2.If two coins are tossed simultaneously, then find the probability that, i)Both are heads ii)Atleast one tail appears 3.Three coins are tossed simultaneously. Find the probability of getting: i)All headsiii)All tails ii)Exactly two headsiv)Atleast 2 headsW10 v)At most 2 heads (Extra) 4.A die is tossed once. Find the probability of an event: i)Getting 3 ii)Not getting 4 iii)Odd number appears (S12 2mks) iv)Prime number appears v)Number greater than 4(W12 2mks) 5.If two dice are thrown; find the probability that the sum of score is 6 or 10.S14 6.If two dice are thrown; find the probability that: i)The sum of two top numbers is an even number ii)The number on both dice are identical iii)The sum of numbers appearing on them is perfect square iv)The sum of the scores is divisible by 4. 7.A card is drawn at random from a well shuffled pack. Find the probability that it is a face card.- 8.A card is drawn at random from a well shuffled pack. Find the probability that it is: i)A black cardiii) a club ii)Ace of hearts or diamondsiv)a diamond or a face card.(W12,S12- 2mks) iii)A king (W13 2mks) 9.Two cards are drawn at random from a well shuffled pack of 52 cards. Find the probability that the cards drawn contain 1 kings & and 1 Queen of the same unit(W12/S142mks) 10.A bag contains 7 white, 5 black and 4 red balls. Find the probability that i)A Ball drawn at random is red or black. ii)Two balls drawn at random are of some colour.SQP, SQPg(type)2mks , W12, W13 11.Inacollegehostelthereare75students,outofwhich15studentsliketodrinktea,40liketo drink coffee and 20 like neither tea nor coffee. Two students come from this hostel to canteen. Find the probability that both will order the same drink. S11 12.ThreemachinesI,IIandIIImanufacturesrespectively0.4,0.5and0.1ofthetotalproduction. The percentage of defective items produced by I, II and III is 2, 4 and 1 percent respectively. For an item chosen at random, what is the probability it is defective?SQPg 13.A room has 3 electric lamps. From a collection of 15 electric bulbs of which only 10 are good, 3 are selected at random and put in the lamps. Find the probability that the room is lighted by at least one of the bulbs.W13 14.AproblemisgiventothreestudentsA,B,Cwhosechancesofsolvingitare 12,34and 14 respectively. What is the chance that the problem is solved?S14