Qnt 561 Week 1 Problem 81

a) The Ludlow Wildcats baseball team, a peasant league team in the Cleveland Indians organization, plays 70 portion of their spiriteds at iniquity and 30 percent during the daytime. The team gathers 50 percent of their iniquitytime games and 90 percent of their day games. According to todays newspaper, they win yesterday. What is the opportunity the game was compete at night? % of games play at night = 70% % of games compete during day = 30% % of night games win =50% % of day games won= 90% hazard of loving = chance of triumphant at night + hazard of attractive during day = % of games play at night x % of night games won + % of games compete during day x % of day games won = 70% x 50% + 30% x 90% = 0. 35 + 0. 27 = 0. 62 chance that the game was played during night condition that the game was won = chance of engaging at night / Probability of kind = 0. 35 / 0. 62 = 35/62 Answer Probability = 35/62 This can be understood in a incompatible wayLet the number of games played be snow bulge of these 100 games, 70 games were played at night and 30 during day Out of 70 games played at night no of games won = 50% x 70 = 35 games and the number of games lost = 50% x 70 =35 Out of 30 games played during day, no of games won = 90% x 30 = 27 games and the number of games lost = 10% x 30 = 3 Thus native games won = 35 + 27 = 62 (Total games lost = 35 + 3 =38, un slight(prenominal) this is non required for calculation) Thus fall out of 62 games won , 35 were won at nightThus opportunity that the game was played at night, given that the game was won = 35/62 b) With each purchase of a gargantuan pizza pie at Tonys Pizza, the customer receives a verifier that can be scratched to forecast if a lettuce leave behind be awarded. The betting odds of benignant a b atomic number 18 patrician take up be 1 in 10, and the odds of agreeable a degage large pizza atomic number 18 1 in 50. You plan to wash up lunch tomorrow at Tonys. What is th e chance 1. That you leave win each a large pizza or a batty fuddle 2. That you will non win a appreciate? 3.That you will non win a prize on three consecutive examines to Tonys 4. That you will win at least virtuoso prize on one of your succeeding(a) three visits to Tonys We have to convert odds into probability Probability = odds / (1+ odds) odds of winning a free soft drink are 1 in 10 Therefore, probability of winning a free soft drink = (1/10) / (1 + 1/10) = 1/11 Odds of winning a free large pizza are 1 in 50 Therefore, probability of winning a free large pizza = (1/50) / (1 + 1/50) = 1/51 What is the probability 1.That you will win either a large pizza or a soft drink The scourts winning a pizza and winning a soft drink are mutually exclusive (since you can either win a pizza or you can win a soft drink but not both at the same time as you have only one coupon ) Probability of winning either a large pizza or a soft drink = Probability of winning a large pizza + Pr obability of winning a soft drink = 1/51 + 1/11 = 62 /561 = 0. 11 or 11% 2. That you will not win a prize? Probability of not winning a prize = 1- Probability of winning a prize = 1- 62/561 = 499/561 = 0. 9 or 89% 3. That you will not win a prize on three consecutive visits to Tonys Since the events of winning / not winning on consecutive visits are independent events we will multiply the probabilities Probability of not winning a prize on three consecutive visits = Probability of not winning on root visit x Probability of not winning on second visit x Probability of not winning on third visit = (499 /561) x (499 / 561) x (499 / 561) = (499/561) 3 = 0. 70 or 70% 4. That you will win at least one prize on one of your next three visits to TonysProbability of winning at least in one case = 1- probability of not winning even once = 1- (499/561) 3 = 0. 30 or 30% c) There are 4 people being considered for the position of chieftain executive officer of Dalton Enterprises. Three of the a pplicants are everywhere 60 years of age. devil are young-bearing(prenominal), of which only one is everywhere 60. 1) What is the probability that a vista is oer 60 and effeminate 2. tending(p) that the candidate is male, what is the probability he is less than 60 3) Given that the somebody is over 60, what is the probability the person is pistillateOut of 4 applicants Male = 2 (both over 60) womanly = 2 (1 over 60, 1 less than 60) 1) What is the probability that a candidate is over 60 and female Out of 4 candidates only 1 is both female and over 60 Therefore probability = ? = 0. 25 or 25% 2. Given that the candidate is male, what is the probability he is less than 60 Both male candidates are over 60 therefore probability = 0 3 Given 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