0
$\begingroup$

Assume that the probability that you find a typo on a given page in any book is approximately $0.0025$. Find an approximation for the probability that in then next $1000$ pages that you read, you will find at least $2$ typos.

I have tried to do $1-P(\text{none}) = 1 - (0.9975)^{1000}$

but this is apparently wrong.

$\endgroup$
  • $\begingroup$ You calculated the probability that in the next $1000$ pages you find at least $1$ typo. They ask for at least $2$ typos. $\endgroup$ – drhab Feb 23 '15 at 9:50
  • $\begingroup$ Yes. $1-P($none$) = P($at least $1)$, not $P($at least $2)$ $\endgroup$ – Graham Kemp Feb 23 '15 at 9:50
  • $\begingroup$ how would i calculate that? would I subtract 1-(1-.9975^1000)? $\endgroup$ – toodles Feb 23 '15 at 9:51
2
$\begingroup$

$1 - P(0)$ means "at least $1$ typo". So you have to find $1 - P(0) - P(1)$. You have $P(0)$ and $P(1)$ can be found as "this page contains $1$ typo, the other pages do not contain any typos * number of all possible permutations", so $P(1) = 0.0025 * (0.9975)^{999} * \binom{1000}{1} = 2.5 * (0.9975)^{999}$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.