DMN currently manages a portfolio of ads for Marketing Direct Analysis (MDA). DMN pays a fee...
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DMN currently manages a portfolio of ads for Marketing Direct Analysis (MDA). DMN pays a fee such that these ads appear in the rotation of ads used by a popular social networking site. The site itself has ads from a wide range of competitors. The site takes a fee per ad to ensure that it is displayed in a user's feed, however the order in which ads are displayed is random. Under a somewhat controversial new policy, MDA wishes to increase the probability that a user will see two consecutive MDA ads at the top of their feed. Here, two ads are considered consecutive if there are no other ads between them, however it is possible that a user may see non-sponsored content. The social media site is regulated such that a user will see exactly one ad per minute, and that once the ads have been used they will not be shown again. The social media site shows all ads that it has been contracted to display. MDA's competitors have 11 ads on the platform, and MDA currently has a portfolio of 6 ads. Every ad is considered 'unique' i.e. there are no repetitions. (a) How many ways can the social networking site arrange these ads? You may leave your solution as a factorial. (b) Show that the probability of the first two ads appearing on the users feed both being MDA ads is 6 x 5 17 x 16 ≈11%. (c) MDA wishes to increase the probability that the first two ads a user sees are MDA ads. How many ads must MDA have in their portfolio with the platform to increase the probability in (b) to 20%? For (c), write down an expression for the probability that the first two ads a user sees are MDA ads, if MDA has a portfolio of m ads. Simplify this to remove the factorials. You may then you may then use guess and check to solve for m if you wish. DMN currently manages a portfolio of ads for Marketing Direct Analysis (MDA). DMN pays a fee such that these ads appear in the rotation of ads used by a popular social networking site. The site itself has ads from a wide range of competitors. The site takes a fee per ad to ensure that it is displayed in a user's feed, however the order in which ads are displayed is random. Under a somewhat controversial new policy, MDA wishes to increase the probability that a user will see two consecutive MDA ads at the top of their feed. Here, two ads are considered consecutive if there are no other ads between them, however it is possible that a user may see non-sponsored content. The social media site is regulated such that a user will see exactly one ad per minute, and that once the ads have been used they will not be shown again. The social media site shows all ads that it has been contracted to display. MDA's competitors have 11 ads on the platform, and MDA currently has a portfolio of 6 ads. Every ad is considered 'unique' i.e. there are no repetitions. (a) How many ways can the social networking site arrange these ads? You may leave your solution as a factorial. (b) Show that the probability of the first two ads appearing on the users feed both being MDA ads is 6 x 5 17 x 16 ≈11%. (c) MDA wishes to increase the probability that the first two ads a user sees are MDA ads. How many ads must MDA have in their portfolio with the platform to increase the probability in (b) to 20%? For (c), write down an expression for the probability that the first two ads a user sees are MDA ads, if MDA has a portfolio of m ads. Simplify this to remove the factorials. You may then you may then use guess and check to solve for m if you wish.
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