# Probability problem for at least two events?

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.

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

$1 - P(0)$ 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 $P(1) = 0.0025 * (0.9975)^{999} * \binom{1000}{1} = 2.5 * (0.9975)^{999}$.