It is Discrete MATH. Three new movies came out this weekend, a movie about space
ID: 3141108 • Letter: I
Question
It is Discrete MATH.
Three new movies came out this weekend, a movie about space, a movie about vampires, and a movie about birds. 50% of people see the movie about birds, 30% of people see the movie about space, and 20% of people see the movie about vampires. Of the people who see the bird movie, 70% buy popcorn. Of the people who see the space movie, 90% buy popcorn. Of the people who see the vampire movie, 40% buy popcorn. Find the probability that a person: a) sees the vampire movie and buys popcorn. b) sees the bird movie and does not buy popcorn. c) who saw the bird movie or the space movie does not buy popcorn. d) bought popcorn. e) who bought popcorn saw the space movie. f) who did not buy popcorn saw the vampire movie or the space movie.Explanation / Answer
(According to Chegg policy, only four subquestions will be answered. Please post the remaining in another question)
a) Probability that a person sees the vampire movie = 20% = 0.2
Probability that a person who sees the vampire movie buys popcorn = 40% = 0.4
=> Probability that a person sees the vampire movie and buys popcorn = 0.2*0.4 = 0.08 or 8%
b) Probability that a person sees the bird movie = 50% = 0.5
Probability that a person who sees the bird movie buys popcorn = 70% = 0.7
Probability that a person who sees the bird movie does not buy popcorn = 1-0.7 = 0.3
=> Probability that a person sees the bird movie and does not buy popcorn = 0.5*0.3 = 0.15 or 15%
c) Probability that a person sees the bird movie = 50% = 0.5
Probability that a person sees the space movie = 30% = 0.3
=> Probability that a person sees the bird movie or the space movie = 0.5 + 0.3 = 0.8
Probability that a person sees the bird movie and does not buy popcorn = 0.15
Probability that a person who sees the space movie buys popcorn = 90% = 0.9
Probability that a person who sees the space movie does not buy popcorn = 1-0.9 = 0.1
Probability that a person sees the space movie and does not buy popcorn = 0.3 * 0.1 = 0.03
=> The probability that a person sees the bird movie or the space movie and does not buy popcorn = 0.15 + 0.03 = 0.18
Therefore, the probability that a person who sees the bird movie or the space movie does not buy popcorn
= 0.18 / 0.8 = 0.225 = 22.5%
d) Probability that a person sees the vampire movie and buys popcorn = 0.08
Probability that a person sees the bird movie = 50% = 0.5
Probability that a person who sees the bird movie buys popcorn = 70% = 0.7
=> Probability that a person sees the bird movie and buys popcorn = 0.5*0.7 = 0.35
Probability that a person sees the space movie = 30% = 0.3
Probability that a person who sees the space movie buys popcorn = 90% = 0.9
=> Probability that a person sees the space movie and buys popcorn = 0.3*0.9 = 0.27
Therefore, the total probability that a person buys popcorn = 0.08 + 0.35 + 0.27 = 0.7 = 70%
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