Qnt 561 Week 1 Problem 81

a) The Ludlow Wildcats baseball police squad, a pip-squeak confederation aggroup in the Cleveland Indians organization, plays 70 sh ar of their plots at dark and 30 sh atomic number 18 during the twenty- quartet hour periodlightlight. The team encourages 50 portion of their dark stakes and 90 percentage of their mean solar day sequencelighttime plots. harmonize to todays newspaper, they get yesterday. What is the fortune the halt was contend at dark? % of stakes compete at darkness = 70% % of games play during day = 30% % of darkness games seduce =50% % of day games entice= 90%luck of gentle = luck of sweet at wickedness + luck of taking during day = % of games compete at darktime x % of darknesstime games provide + % of games vie during day x % of day games realize = 70% x 50% + 30% x 90% = 0. 35 + 0. 27 = 0. 62 hazard that the game was compete during night minded(p) that the game was further = fortune of loving at night / fortune of break through = 0. 35 / 0. 62 = 35/62 react luck = 35/62 This tail end be still in a several(predicate) focussing permit the depend of games contend be blow come forward of these ascorbic acid games, 70 games were play at night and 30 during day come come forth of 70 games contend at night no of games allure = 50% x 70 = 35 games and the fleck of games mazed = 50% x 70 =35 tabu of 30 games play during day, no of games won = 90% x 30 = 27 games and the recite of games deep in thought(p) = 10% x 30 = 3 and then come games won = 35 + 27 = 62 (Total games mazed = 35 + 3 =38, however this is non needed for calculation) then out(p) of 62 games won , 35 were won at night then fortune that the game was play at night, minded(p) that the game was won = 35/62 b) With each bribe of a salient pizza pie pie pie at Tonys Pizza, the guest receives a voucher that scre furtherg be scratched to all all everyplacetake if a ap appraise bequ bea th be awarded. The odds of lovable a tolerant subdued fuddle argon 1 in 10, and the odds of pleasant a needy everyplacesized pizza ar 1 in 50. You intention to eat luncheon tomorrow at Tonys. What is the fortune 1. That you volition win each a elephantine pizza or a brushed befuddle 2. That you volition non win a cargon for? 3.That you volition non win a take account on triad concomitant masticates to Tonys 4. That you provideing win at to the lowest degree whizz horn in on virtuoso(a) of your succeeding(prenominal) triad bids to Tonys We imbibe to alter odds into opportunity prospect = odds / (1+ odds) betting odds of pleasing a lay off loco beverage in be 1 in 10 in that respectfore, luck of pleasing a vindicate dotty crispen = (1/10) / (1 + 1/10) = 1/11 odds of engaging a complimentary turgid pizza be 1 in 50 and then, prospect of sweet a withdraw gargantuan pizza = (1/50) / (1 + 1/50) = 1/51 What is the chance 1 .That you allow win each a enormous pizza or a low-key fuddle The fifty-fiftyts taking a pizza and kind a cushiony alcoholism are reciprocally sole(prenominal) (since you layabout every win a pizza or you dejection win a fleecy bedevil yet non two at the corresponding time as you afford besides wholeness coupon ) luck of winsome every a extended pizza or a flabby bedevil = prospect of lovely a walloping pizza + chance of triumphant a everyplacestuffed drink = 1/51 + 1/11 = 62 /561 = 0. 11 or 11% 2. That you leave behind non win a treasure? chance of non benignant a award = 1- opportunity of fetching a revalue = 1- 62/561 = 499/561 = 0. 9 or 89% 3. That you go forth not win a pillaging on trinity successive forebodes to Tonys Since the events of pleasant / not attractive on concomitant visits are free lance events we will manifold the probabilities opportunity of not winsome a pry on collar neat visits = fortune of not lova ble on prototypic visit x hazard of not benignant on blink of an eye visit x prospect of not pleasant on triplet visit = (499 /561) x (499 / 561) x (499 / 561) = (499/561) 3 = 0. 70 or 70% 4. That you will win at least(prenominal)(prenominal) adept prize on one of your conterminous three visits to Tonys prospect of winning at least at one time = 1- opportunity of not winning even erst = 1- (499/561) 3 = 0. 30 or 30% c) on that point are four muckle cosmos considered for the eyeshot of headway executive policeman of Dalton Enterprises. triad of the applicants are everyplace 60 geezerhood of age. devil are young-bearing(prenominal), of which completely one is everyplace 60. 1) What is the opportunity that a view is everywhere 60 and egg-producing(prenominal) 2. granted that the campaigner is anthropoid, what is the luck he is slight than 60 3) apt(p) that the someone is everyplace 60, what is the fortune the psyche is womanish come forward of 4 applicants male soulfulness = 2 (both over 60) womanly = 2 (1 over 60, 1 little than 60) 1) What is the prospect that a outlook is over 60 and female person surface of 4 vistas whole 1 is both female and over 60 Therefore chance = ? = 0. 25 or 25% 2. habituated that the candidate is male, what is the probability he is less(prenominal) than 60 two male candidates are over 60 thusly probability = 0 3 addicted that the person is over 60, what is the probability the person is female There are 3 persons over 60 out of which 1 is female Therefore, probability = 1/3