Name: _hevatin, Aiyéra O_ Date:_o'& Tore 2090 Score: Section Exercise 5.9 1. The number of accidents that occur at an express way is Poisson distributed with a ‘mean of $ pet week. Find the probability of no accidents in one week. . Aes Plawod: AX yo woe ee A carr |pexsa= v.07 | ! [Berta cts, ao “7 2. Rainfalls occur randomly and independently over the course of Metro Manila. The average is 8 rainfalls every month. What is the probability of at most one rainfall in a month? Solution: {> P lar mart ene paingon) + Pleo) ¢ Pixs) 8 > ee 1 g® as yg sls on fet r 209s + D.00 me O-be 3018 3, The average number of automobiles per minute stopping for gas at a particular service station along the Coastal Road is 4. What is the probability that in any given minute more than two automobile will stop for gas? Solution: 4.4 Pomore hana porr2) 4 Plea) 4 P xe 4) r Bae yor oes) sg 3a ryt ; pel get - wt ar 2 omits 01403 4 0.1963 [east] 4, His ona new business website occur quite infrequently. They occur randomly and independently with an average of six per week. Find the probability that the site gets more than 3 hits in a week. Solutions: > 3 Pemoee phan shirs)= Plx> 2)4 Plx=4) +P (ea 4 Pixsu) Pes 73? 40-9 3 =e Fe, ote a” ar 20-2244 0-1US EDI Fo OMdYName: _Mnncitu, aiytra_O. Date:_2) ocroeen 2020 Score: Section Exercise 5.8 1. A survey found that one out of four Filipinos says he or she has visited a dentist in any given month. If 12 people are selected at random, find the probability that exactly five will have visited a dentist last month. Solution: fine = ont ant Po ne Pixdz ot pa’ 103 | oe a3 Pus (9. ash cor (apes! 2. Ina survey, 80% of the people interviewed were unaware that maintaining a healthy lifestyle could reduce the risk of diabetes. If 18 people are selected at random, find the probability that exactly ten are unaware that maintaining a healthy lifestyle could reduce the risk of diabetes. Solution: POD? HE iggy wh” el Wor 10)? 10 ar le Wes Pus) = 0.012 4208702 3. Ina survey conducted by the office of student affairs, 2 out of 5 students aid that office show “little concer” for students. Find the probability that at most three out of eight randomly selected students will agree with this statement. Solution: shasajene en Pre) 2 tou)’ (ou? fons wren Pie) ¢P0 4 P18) 9 PED qe rod? wate tie cseal 7 Od o.cgdryo-200 are Prode oy — 49 21G6 4 PD» Ok, 34 Pu) = em toa touF oe woptouP? >[e 71 | 4. A survey from independent agency found that 40% of consumers receive their spending money from their other jobs. If 6 people are selected at random, find the ity that at ei often ding money rom their other obs. Solution: yyy > Ut join (ous Pl) = oa (oy! coo? fro4 ee =a a Gare mu 4, hee 23%, Psd.» Oz, re ee % ou Pw) > oak wif THERE FORE ene Pu) Feud) 4 P(E) = 0-329 + 00364 wp gare Pad 364,4, Am insurance company insures a house worth 3,500,000 for an annual premium of 20,000. If the company figures that the probability of the house being burned down by fire is 0.005, what will be the company’s expected profit? Solution: ovrcome “utonce | 0,000 | EXPECTED vauve (3.990,000) 1:5) + {0,000)( 6-486) cos | 04s axpecrep wu? 2,00 PER yeok MT the PROFIT oF the company 5. A financial executive believes that each savings account customer has, on average, two credit cards, The following distribution represents the number of credit cards people own. Find the mean, variance, and standard deviation. Is the financial executive correct? ‘Number of credit cards X 0 1 2 3 4 Probability P(X) 0.19 0.50 0.18 0.08 0.05 Solution: wenn > 2[ x: 260] = Olo-1a) 4 So.sod4 20RD 91 0-08)4 HIP os) ZT xt Poy] eon? 7 7 0%(p 40) (x0) 4770-184 37K 2-08) talpee)~ 13 emnpead osmenon® Shop sey 6. The Movies and Television Regulatory and Classification Board (MTRCB) determined the number of commercials shown in each of the four night programs over a period of time. Find the mean, variance, and standard deviation for the distribution shown. ————— - 10 i 12 13 Probability POX), 0201030 035 [ois Solution: mee = (0-26) 4 11(0.9024 12 (0-3) + 1310-15) roeHYE MMS v7 93s) 4 a wogimytes 110-2004 IO-De)A INL O-DE)S BOA) > WHE vARmnce > 0 ar StxpaRD pevenon > VO-AL pi EESName: _MAncitin, Alyssa O- Date:_2i0c10®8R2020_Seore:, Section Exercise 5.7 1. A lottery offers one 500,000 prize, two P100,000 prizes, and four P25,000 prizes. Fifty thousand tickets are sold at P50 each, Find the expectation if a person buys 25 eke? pePECTED vrLVEt Selman = 00,000 ( "450,000 + 1001000 ovteone (4/50, 000) + 26,00 ( 4/sv,000) PR 0R Ty F104 442 beens PIU he qhe expected hesepoRe 284 fi) =P yoo 1250 volt in 4 tickey FPO ie the expecttel 10K oF wing o Tickers 2. Ifa person rolls a pair of dice and gets a sum of 7 or 8, he wins P750. If the person Bets a 6 or 9, he wins P500. The cost to play the game is P100. Find the expectation of the game, EXPECTED VLVE# ary (1/30) 4.200 ( Vy) Solution: = 270.1614 12e 2 Pasd.juq Fssdiut — Py 2 Posy. wt iv the expected winning in playing the game 3. The number of jackets sold per week at a boutique shop is shown in the table, with the corresponding probabilities. Find mean, variance, and standard deviation of the distribution. Number ofJacketsSoldX [19 [15 _]18 [12] 16 Probabilit 0.24 | 0.36 0.11 0.10 0.20 If the manager of the boutique shop wants to be sure that he has enough jackets for the next month, how many should the manager purchase? Solution: ean: = [ x- Pu) ] F 14 (0.24) y (0-34) +1 (O41) 412(0-10) FI CO.20) Ww3d, Varionce s = [ X*+P (x) }- mean™ 2 + 19%(0.24) 4 16" p.30)4194(0.1) 412" L0-10) 116(0-20) ~ [Ju 34) ee, STANDARD DevinTOn= J7-%S F499 —_—# varianc4. Using the sample space for tossing a pair of dice, construct a probability for the sums Prot of 2 through 12. Solution: Ov come a|3 f$\ ojo te | w\ 2 protreuny | Yel Viel Ye! Val */5e | Yu 1/34 Yn Whe 5. Construct a probability distribution for a family of four children. Let X represent the number of girls. Solution: NO OF eres oo PROBE BILITY Pu)Name: _nenqu.ca, ALyhn_0. Date:_2 0cTOBE? 2020 ___ Score: Section Exercise 5.5 and 5.6 1. In a RFS Housing Plan, 48% of the houses have a terrace and a parking space, 64% have a terrace. Find the probability that a house has a parking space, given that it has a terrace. Solution: 9 (f79° Pit4F) , O48 ge 1% | Ts TeRRace Pin) Oud Pe Porking 2. At Centro Escolar University, the probability that a student takes statistics and is on dean's list is 0.055. The probability that a student is on the dean’s list is 0.25. Find the probability that the student is taking statistics, given that he or she is on the dean’s list, Solution: Pisip)= PLS@P) . oF - 6 99 og © Sanenes PUP) 0-25 De Denws Let 3. Three hundred employees were selected from Makati City private companies, and they were asked whether or not they have any retirement benefits provided by their ‘companies. Based from this information, the following two-way classification table was prepared. Gender, ‘Have Retirement Benefits | Do not have Retirement Benefits | Tort Man 90 120 uC: Woman 60. 30, av TOTHL 1S 150 ‘300 Suppose one employee is selected at random for these 300 employees. Find the probability that the respondent has retirement benefits, given that the respondent is a man. Solution: p (vam): p(m ew ap [300 PUR) * 210/300 03 man WA: w/ 8 ebpemon bene rit10. If two cards are selected from a standard deck of 52 cards without replacement, find these probabilities (a) both are hearts, (b) both are the same suit, (c) both are jacks, (d) 1 is an ace and 1 is a queen. Solution: a op, a4 Fintan) 22 2 em sound # A xa St b. Pram it) 2 (Bw) d Peace eaveen) ?— a 1 (+) 4 A] “TA| ou, 11. Seven married couples are in a party. If two are chosen at random, find the probability that (a) they are married, (b) one is male and one is female. Solution: DA peamied)= 1. 1 P-Plowenates repenate) = IC, * 101 wer 4 Wee jz “44 B a) 12. Consider the 70 households that purchased a DVD player, 48 households are satisfied with their purchase and 22 households are dissatisfied. Suppose two households are randomly selected from the customers. Find the probability that both households are dissatisfied with their purchase. Solution: Peweh diecariepied) 2 22, «34 ‘Tb v4 = Aun 4930 uy Ww6. These are 40 students in a class with 23 male students. What is the probability that two selected students are female? Solution: Female > 40-23 Female 2 re, P (nwo Femare endom celecred) = Pli1.2) : Wem _ 22 _ pa Pt42) yey Ie 7. Consider that random experiment of tossing a coin four times, What is the probability of the event that exactly two of the coin tosses come out tails? Solution: Prexoory mworeitd = 0 1 Tom Rein: 2° 2242 uy 8. Two incandescent lights are chosen at random from 19 lights of which 4 are defective. Find the probability that (a) none is defective? (b) exactly one is defective? Solution: Prexaerly move = si). OC & punone alepective) b he ed dete ete: > cug) cata) = 1e(a) = ps il ni” oy 9. Two cards are selected at random from 10 cards numbered 1 to 10. Find the probability that the sum is even if the two cards are drawn one after the other without replacement. Solution: Pa este e(,2) = 15 ODP opzeRN vy 7 C(S.2)5 19 cre even? Saha cop + EVEN # opp x 0 unyt3. Suppose that we roll a pair of dice. What is the probability that these will be at least one die coming up 1? Solution: Way 012) U3 G4) G5) 04) Prar veart ont n (ot) (2 (243) 2 4) (2,3) (2, ae, come * 13 mene 10.9 2) 3) BO GS BO) wD ou eprce 7) HA) 129) Gg) a) gS) (si) (29) (3,0) Us) 64) 5,6) WD BO BOWED (Cr ws (») P) 4: A giz parr er sx toppings-b42dn, small meatballs, mushroom, peYperoni, , and that can be put on their basic cheese pizza. What is the probability of choosing two toppings but not having ham or bacon toppings? Solution: _ (8, $) (0,49)(B PLB H)( 84 (Hm) Ploer raving ram /toocen) fi] tonne. | (gm, (8,4) (690,59 (1.29109, cma wk G0) CP.) (POH) }. The result of the survey about the new policy on school uniform is shown in the table. Gender Favor Oppose No Opink rem Male 2B WW 3 34 Female 22 9 15 de Tora as 20 0 =e If a student is selected at random, find these probabilities (a) given that the student is a male, opposes that new policy on school uniform, (b) given that the student favors the new policy on school uniform, the student is a female. Solution: % Plow: Poweo) Pl) > Pleven), 2 - Pir) PO) = es bsName: revo, Alyssa 0. Date:_210C12R 2020 Score: Section Exercise 5.4 A. State which events are independent and which are dependent. 1, Drawing a card from a standard deck and tossing a coin. INDEPENDENT 2. A mother being left-handed and the height of a daughter. PENDENT 3. Having a small shirt size and having a high IQ level. WDEPEND ENT. 4, Driving on wet roads and having an accident. DEPENDENT 5. Getting a retirement pay and purchasing a new car. WDE PENDENT 6. Drawing a ball from a box, without replacement, and thendrawing a second ball. DEPENDENT 7. Having a mobile phone and having a sim card. Defenpent 8. Having a LCD TV and having a DVD player. DEPEN DEN: B. Solve the following: 1, Find the probability of obtaining an odd number in one roll of die. Solution: buteome 4,23, 4,5, 6 23 somne Provo) > ME PACE! fF 1,0,3,y,0 6} 2. A die is rolled once. What is the probability that (a) a number less than 4 is obtained? (b) a number of 2 to 5 is obtained? Solution: a b. Plemsy= 4 Priest tHew 4) C-Name:_nanciun, Alyssa @ Date:_210CT08ER2020 Score: Section Exercise 5.3B Find the probability of obtaining an even number in one roll of a die. Solution: ee Feeven umber) > Daye [+] e 2) .. A ball is drawn at random from a box containing 4 red balls, 5 white balls, and 3 green balls, Determine the probability that it is (a) red (b) white (c) not white (d) not © Poor wnitey 2 In Pwhirey | [4 y l-spa 2 4. Rroer geeern = 1 = Plgaten) 2 A multiple-choice question on a test has four choices. If Uzziel choose one answer based on “pure guess” what is the probability that his answer is (a) correct? (b) wrong? Solutior 2 Ficenenie? fi] . Peapong) =| ; . A call center company has a total of 120 agents and 45 are men. What is the probability that a randomly selected call center agent from the company is a (a) ‘women? (b) men? Solution: @ Piwomeny: Io-ds IS. Pome = AL © 720 320 . A random sample of 1,750 adults showed that 850 of them have surf the intemet at least once in a week. What is the probability that a randomly selected adult has surf the intemet? Solution: Ploduls) = 99. [a S150 35Name: _yancnta, aiysca_O- Date:_2v0cTeER 2020 Score: Section Exercise 5.2B Evaluate the following: ie TPG) sh. HLENMLENS)WOCYNDL) 4 2) 33! BE 23 = SUDO er Gi. 8.21+P (6,3) = 20) 4 Ut (A ONGE/N OME} |IAN 4192009 : St 419,001, #0o +U 2204 visip tar tat « [wa) aaa 9.C(9,4) =_B_ Cx WenLay(ary - MEN OM Bay? Bey $08 205-24 F UMN’ = (Yo, 240 BNTOTO a) FADD 10.C(13, 10) 8! . ar [arr] [ e2007]f 202) {-1yrot | “3007 46 12) 3u2)0) Det eB) 8 . 5P,4) = 8, 11. 51+C(B,2) = 51: +_@ a sth aa & womowary + 1204 Sty hery sae 0270) -[ev0 7 (4g) 6P(I,9) nt) om 12. P(3, 1) + C(4, 2) = te Tay? RODEO 5s ean F MLLNENINE ETT | gra yines Des ae wn 4, 52. 900. fa