Qnt 561 Week 1 Problem 81

a) The Ludlow Wildcats baseball team, a minor league team in the Cleveland Indians organization, plays 70 part of their games at shadow and 30 portion during the day. The team wins 50 percent of their night games and 90 percent of their day games. According to todays newspaper, they win yesterday. What is the opportunity the game was play at night? % of games compete at night = 70% % of games played during day = 30% % of night games won =50% % of day games won= 90% hazard of benignant = Probability of amiable at night + Probability of attractive during day = % of games played at night x % of night games won + % of games played during day x % of day games won = 70% x 50% + 30% x 90% = 0. 35 + 0. 27 = 0. 62 Probability that the game was played during night given that the game was won = Probability of winning at night / Probability of winning = 0. 35 / 0. 62 = 35/62 Answer Probability = 35/62 This goat be mum in a different wayLet the number of games played be 100 erupt of t hese 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 woolly-headed = 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 frankincense total games won = 35 + 27 = 62 (Total games lost = 35 + 3 =38, but this is not required for calculation) Thus kayoed of 62 games won , 35 were won at nightThus chance that the game was played at night, given that the game was won = 35/62 b) With each purchase of a astronomic pizza pie at Tonys Pizza, the customer receives a coupon that can be scratched to jaw if a prize ordain be awarded. The betting odds of winning a free soft confuse are 1 in 10, and the odds of winning a free large pizza are 1 in 50. You plan to eat lunch tomorrow at Tonys. What is the probability 1. That you will win either a large pizza or a soft drink 2. That you will not win a prize? 3.Tha t you will not win a prize on three consecutive visits to Tonys 4. That you will win at to the lowest degree whizz prize on bingle of your next three visits to Tonys We have to interchange odds into probability Probability = odds / (1+ odds) Odds of winning a free soft drink are 1 in 10 in that locationfore, 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 events winning a pizza and winning a soft drink are mutually soap (since you can either win a pizza or you can win a soft drink but not two at the same time as you have only unmatchable coupon ) Probability of winning either a large pizza or a soft drink = Probability of winning a large pizza + Probability 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 first-class honours degree visit x Probability of not winning on routine visit x Probability of not winning on trinity 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 once = 1- probability of not winning even once = 1- (499/561) 3 = 0. 30 or 30% c) There are four throng being considered for the position of chief executive officer of Dalton Enterprises. Three of the applicants are over 60 years of age. Two are distaff, of which only one is ove r 60. 1) What is the probability that a candidate is over 60 and pistillate 2. attached that the candidate is manlike, what is the probability he is less than 60 3) assumption that the person is over 60, what is the probability the person is pistillateOut of 4 applicants Male = 2 (both over 60) Female = 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