Qnt 561 Week 1 Problem 81

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a) The Ludlow Wildcats baseball team, a minor league team in the Cleveland Indians organization, plays 70 percent of their games at night and 30 percent during the day.  The team wins 50 percent of their night games and 90 percent of their day games.  According to today's newspaper, they won yesterday.  What is the probability 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%

Probability of winning
= Probability of winning at night + Probability of winning 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 can be understood in a different way
Let the number of games played be 100
Out 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 total games won = 35 + 27 = 62

(Total games lost = 35 + 3 =38, but this is not required for calculation)

Thus out of 62 games won , 35 were won at night
Thus probability that the game was played at night, given that the game was won = 35/62

b) With each purchase of a large pizza at Tony's Pizza, the customer receives a coupon that can be scratched to see if a prize will be awarded.  The odds of winning a free soft drink are 1 in 10, and the odds of winning a free large pizza are 1 in 50.  You plan to eat lunch tomorrow at Tony's.  What is the probability: 1. That you will win either a large...
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