For a monthly subscription fee, a video download site allows people to download and watch up to five
movies per month. Based on past download histories, the following table gives the estimated probabilities
that a randomly selected subscriber will download 0, 1, 2, 3, 4 or 5 movies in a particular month.
Number of downloads 0 1 2 3 4 5
Estimated probability 0.03 0.44 0.24 0.10 0.10 0.09
If a subscriber is selected at random, what is the estimated probability that this subscriber downloads the
following amount of movies?
(a) three or fewer movies
(b) at most three movies
(c) four or more movies
(d) zero or one movie
(e) more than one movie
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(a) To find the estimated probability that a subscriber downloads three or fewer movies, we need to sum the probabilities of downloading 0, 1, 2, or 3 movies.
Estimated probability = 0.03 + 0.44 + 0.24 + 0.10 = 0.81
The estimated probability that a subscriber downloads three or fewer movies is 0.81.
(b) To find the estimated probability that a subscriber downloads at most three movies, we need to sum the probabilities of downloading 0, 1, 2, or 3 movies.
Estimated probability = 0.03 + 0.44 + 0.24 + 0.10 = 0.81
The estimated probability that a subscriber downloads at most three movies is 0.81.
(c) To find the estimated probability that a subscriber downloads four or more movies, we need to sum the probabilities of downloading 4 or 5 movies.
Estimated probability = 0.10 + 0.09 = 0.19
The estimated probability that a subscriber downloads four or more movies is 0.19.
(d) To find the estimated probability that a subscriber downloads zero or one movie, we need to sum the probabilities of downloading 0 or 1 movie.
Estimated probability = 0.03 + 0.44 = 0.47
The estimated probability that a subscriber downloads zero or one movie is 0.47.
(e) To find the estimated probability that a subscriber downloads more than one movie, we need to sum the probabilities of downloading 2, 3, 4, or 5 movies.
Estimated probability = 0.24 + 0.10 + 0.10 + 0.09 = 0.53
The estimated probability that a subscriber downloads more than one movie is 0.53.
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