Problem 2 (20 points). Suppose you go to your neighborhood \"RedBox\" to select
ID: 2921439 • Letter: P
Question
Problem 2 (20 points). Suppose you go to your neighborhood "RedBox" to select a movie "RedBox" is not functioning properly. Instead of selecting the movie of your choice, you movies at random from a collection of 10 different movies: 4 New Releases, 3 Action Movies, 2 and 1 Foreign Film. Define the following events: will receive two Comedies, A: Event A occurs when one of the two movies you receive is a Foreign Film. B: Event B occurs when the two movies you receive are from different categories (i.e. New Release and Action). C: Event C occurs when neither of the two movies you receive is a New Release. a) How many different combinations of two movies are possible? b) Compute P(A)Explanation / Answer
a) First movie can be chosen in 10 ways, and the second one in 9 ways. thus total ways of choosing two movies is 10*9 =90
b) ways of choosing a foreign movie is 1, any other movie can be chosen in 9 ways
Total ways of choosing 2 movies out of 10 is 10C2=10*9/2=45
thus answer is 9/45=1/5
c) p(B|A)=P(B) if A and B are independent. thus P(B)=probability of choosing movies from different categories.
(4*3+4*2+4*1+3*2+3*1+2*1)/45=0.78
d) P(A union C)=P(one of the 2 movies is foreign film OR neither is New Release) =P(one of the two movies is foreign film)+P(neither is new release)- P(one of the 2 movies is foreign film AND neither is New Release) =1/5 + (3*2+3*1+2*1)/45 - (3*2)/45 =0.311