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We have two options for serving ads within Newsfeed:

1 - out of every 25 stories, one will be an ad
2 - every story has a 4% chance of being an ad
For each option, what is the expected number of ads shown in 100 news stories?
If we go with option 2, what is the chance a user will be shown only a single ad in 100 stories? What about no ads at all?

User Lakeweb
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1 Answer

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Final answer:

In both options 1 and 2, the expected number of ads in 100 news stories is 4. Option 2 yields a probability of 1.75% for exactly one ad, and 1.70% for no ads.

Step-by-step explanation:

Expected Number of Ads in News Stories

For option 1, where 1 out of every 25 stories is an ad, the expected number of ads shown in 100 news stories would be 4, as 100 divided by 25 equals 4.

For option 2, with a 4% chance of any story being an ad, the expected number of ads shown in 100 news stories would be 100 multiplied by 0.04, which is also 4.

Probability of Viewing a Specific Number of Ads

To calculate the probability of a user being shown only a single ad in 100 stories with option 2, we use the binomial probability formula:

P(X=1) = (100 choose 1) * (0.04)^1 * (0.96)^99

This equals approximately 0.0175, or 1.75%.

The chance of no ads being shown at all can be calculated as (0.96)^100, which equals approximately 0.0170, or 1.70%.

User Esteban Filardi
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