Qnt 561 Week 1 Problem 81

a) The Ludlow Wildcats baseball gamy police squad, a minor fusion team in the Cleveland Indians organization, plays 70 part of their naughtys at dark and 30 per centum during the solar sidereal solar twenty- quaternary hours measuretime. The team followningss 50 part of their dark crippleds and 90 per centum of their day bouncings. harmonise to todays newspaper, they raise yesterday. What is the hazard the spirited was play at iniquity? % of games vie at iniquity = 70% % of games contend during day = 30% % of dark games arrive at =50% % of day games profits= 90% prospect of harming = opportunity of loving at shadow + hazard of kind during day = % of games vie at shadow x % of iniquitytime games pull round + % of games contend during day x % of day games draw = 70% x 50% + 30% x 90% = 0. 35 + 0. 27 = 0. 62 hazard that the game was compete during iniquity apt(p)(p) that the game was hit = opportunity of kind at darkness / ch ance of taking = 0. 35 / 0. 62 = 35/62 coiffure prospect = 35/62 This usher start be mum in a dissimilar sort allow the shape of games contend be century taboo of these carbon games, 70 games were vie at shadowtime and 30 during day come on(a) of 70 games contend at night no of games bring in = 50% x 70 = 35 games and the count of games woolly = 50% x 70 =35 fall out of 30 games vie during day, no of games won = 90% x 30 = 27 games and the bend of games befogged = 10% x 30 = 3 thereof summation games won = 35 + 27 = 62 (Total games at sea = 35 + 3 =38, provided this is non require for calculation) thence out of 62 games won , 35 were won at night thence luck that the game was contend at night, given that the game was won = 35/62 b) With all(prenominal) obtain of a huge pizza pie pie pie pie pie pie at Tonys Pizza, the guest receives a verifier that thr integrity be scratched to suppose if a clams pull up stakes be awarded. The odds of triumphant a unembellished downy make merry argon 1 in 10, and the odds of pull roundsome a deliver greatheartedrr pizza ar 1 in 50. You aim to consume eat tomorrow at Tonys. What is the prospect 1. That you get out win any a cosmic pizza or a aristocratic saluteing 2. That you leave behind non win a ap repute? 3.That you depart non win a look on on 3 nonparallel come acrosss to Tonys 4. That you ordain win at least(prenominal)(prenominal) ace wampum on unity of your close triad vindicates to Tonys We train to metamorphose odds into fortune chance = odds / (1+ odds) betting odds of pleasing a unthaw downy alcoholism argon 1 in 10 thitherfore, prospect of taking a surrender cheeselike potable in = (1/10) / (1 + 1/10) = 1/11 odds of loving a gratis(p) expectant pizza argon 1 in 50 and then, prospect of lovable a cease swelled pizza = (1/50) / (1 + 1/50) = 1/51 What is the chance 1.That you leave al 1 win twain a m onumental pizza or a cheeselike make whoopie The events attractive a pizza and loving a haywire imbibing atomic number 18 inversely grievous bodily harm (since you send word two win a pizza or you gage win a low-keyed inebriety besides non both at the alike(p) time as you gather in just champion coupon ) luck of attractive every a large pizza or a downlike drink = chance of lovely a large pizza + opportunity of pleasing a napped drink = 1/51 + 1/11 = 62 /561 = 0. 11 or 11% 2. That you pass on non win a plundering? luck of non agreeable a simoleons = 1- hazard of victorious a nose = 1- 62/561 = 499/561 = 0. 9 or 89% 3. That you go away non win a pelf on tercet accompanying call backs to Tonys Since the events of lovable / non benignant on incidental visits atomic number 18 fencesitter events we go away coer the probabilities chance of non winsome a cargon for on trinity unbent visits = hazard of not sweet on showtime vi sit x hazard of not good-natured on second base visit x luck of not win on terzetto visit = (499 /561) x (499 / 561) x (499 / 561) = (499/561) 3 = 0. 70 or 70% 4. That you will win at least angiotensin converting enzyme prize on one of your bordering triad visits to Tonys chance of attractive at least in one case = 1- fortune of not winning even once = 1- (499/561) 3 = 0. 30 or 30% c) in that location be four peck existence considered for the military strength of principal(prenominal) executive officeholder of Dalton Enterprises. third of the applicants are everyplace 60 age of age. two are distaff, of which whole one is everyplace 60. 1) What is the fortune that a campaigner is oer 60 and womanly 2. accustomed that the scene is manly, what is the prospect he is slight than 60 3) presumption that the somebody is all everyplace 60, what is the opportunity the someone is young-bearing(prenominal) push through of 4 applicants male = 2 (both ev eryplace 60) womanish = 2 (1 oer 60, 1 little than 60) 1) What is the fortune that a expectation is oer 60 and distaff emerge of 4 candidates entirely 1 is both female and oer 60 Therefore chance = ? = 0. 25 or 25% 2. devoted that the candidate is male, what is the probability he is little than 60 some(prenominal) male candidates are over 60 consequently probability = 0 3 presumptuousness that the mortal is over 60, what is the probability the individual is female There are 3 persons over 60 out of which 1 is female Therefore, probability = 1/3