1. A new three-screen cinema has just opened in the town of Quirpoon. The table
ID: 2903098 • Letter: 1
Question
1. A new three-screen cinema has just opened in the town of Quirpoon. The table summarizes the fraction of customers attending each of the three movies showing on a given night and, for each film, the fraction who purchase popcorn.
Find the probability that
a. A randomly selected patron attends La Vie dum Elan and purchases popcorn;
b. A randomly selected patron attends Rarer Birds and does not purchase popcorn;
c. A randomly selected patron purchases popcorn;
d. A customer attending Rarer Birds or Codroy Vampire Project does not purchase popcorn;
e. A customer who attends La Vie dun Elan purchases popcorn
Explanation / Answer
a) P(attending la vie d'un elan) = 0.2 ; P(purchasing popcorn | attending vie d'un elan) = 0.4
Since P(A|B)=P(A intersection B) / P(B), we get: P(A intersection B) = P(A|B)*P(B).
Thus P((attending la vie d'un elan) and (purchasing popcorn)) = (0.4)*(0.2) = 0.08
b) P(attending rarer birds) = 0.5 ; P(purchasing popcorn | attending rarer birds) = 0.7
Therefore: P(NOT purchasing popcorn | attending rarer birds) = 1 - 0.7 = 0.3
Thus P((attending rarer birds) and (NOT purchasing popcorn)) = (0.5)*(0.3) = 0.15
c) P(purchasing popcorn) = P(purchasing popcorn | attending rarer birds)*P(attending rarer birds) + P(purchasing popcorn | attending codroy vampire)*P(attending codroy vampire) + P(purchasing popcorn | attending la vie d'un elan)*P(attending la vie d'un elan)
= (0.7)*(0.5) + (0.9)*(0.3) + (0.4)*(0.2) = 0.7
d) P(Not purchasing popcorn| attending rarer birds or codroy vampire) = P(Not purchasing popcorn| attending rarer birds) + P(Not purchasing popcorn| attending codroy vampire)
= 0.3 + 0.1 = 0.4
e) P(purchasing popcorn| attending la vie d'un elan) = 0.4
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