0
$\begingroup$

If 72% percent of new apps are reviewed within the last 7 days, then there is a 72% chance that any app is reviewed in the last week.

$$72\% = \sum\limits_{i = 0}^{6} {x\left( {1 - x} \right)^i }$$
          where $x$ represents the probability that an app is reviewed each day.

If $p = \left( {1 - x} \right)$, then the following is true:

$ \eqalign{ & 72\% = x + xp + xp^2 + xp^3 + xp^4 + xp^5 + xp^6 \cr & 72\% = x\left( {1 + p + p^2 + p^3 + p^4 + p^5 + p^6 } \right) \cr & 72\% = 1 - p^7 \cr & p^7 = 1 - 72\% \cr & p^7 = 28\% \cr & \left( {1 - x} \right)^7 = 28\% \cr & 1 - x \approx 0.8337 \cr & x \approx 16.63\% \cr} $

Is my work correct?

  • 0
    Is this a plug for Apple?2010-10-29
  • 0
    What's a plug? And no, this is just me doing math...2010-10-29

1 Answers 1

2

Looks good. You have made the assumption, probably incorrect, that the probability of an app being reviewed is independent of the time since release and independent of whether it has already been reviewed. But for math problems (as opposed to the real world) we often assume such.