Qnt 561 Week 1 Problem 81

a) The Ludlow Wildcats baseball police squad, a churl league team in the Cleveland Indians organization, plays 70 percent of their plots at darkness and 30 percent during the day. The team coaxs 50 percent of their night games and 90 percent of their day games. According to todays newspaper, they won yesterday. What is the chance the game was played at night? % of games played at night = 70% % of games played during day = 30% % of night games won =50% % of day games won= 90% opportunity of taking = Probability of win at night + Probability of kind 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 give that the game was won = Probability of win at night / Probability of winning = 0. 35 / 0. 62 = 35/62 Answer Probability = 35/62 This can be understood in a different wayLet the number of games played be cytosine Ou t 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 pith games won = 35 + 27 = 62 (Total games lost = 35 + 3 =38, but this is non postulate for calculation) Thus out of 62 games won , 35 were won at nightThus probability that the game was played at night, given that the game was won = 35/62 b) With each grease one(a)s palms of a large pizza at Tonys Pizza, the customer receives a coupon that can be scratched to settle if a dough lead be awarded. The odds of winning a muster out soft wassail be 1 in 10, and the odds of winning a step down large pizza be 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 threesome consecutive visits to Tonys 4. That you will win at least one prize on one of your bordering 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 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 exclusive (since you can either win a pizza or you can win a soft drink but not both(prenominal) 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 + 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 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 formerly = 1- probability of not winning even once = 1- (499/561) 3 = 0. 30 or 30% c) There are four people being considered for the position of chief executive officer of Dalton Enterprises. Three of the applicants are everywhere 60 years of age. Two are female, of which only one is oer 60. 1) What is the probabil ity that a candidate is over 60 and female 2. Given that the candidate is male, what is the probability he is little than 60 3) Given that the person is over 60, what is the probability the person is femaleOut 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