# Thread: mistakes probability

1. ## mistakes probability

See you are typing a research paper and the average number of spelling grammatical mistakes per page is 6, while the standard deviation is 2. What is the probability of having more than 20 mistakes on the page?

2. ## Re: mistakes probability

Unless you assume some underlying distribution you can't really calculate this.

You can bound it though.

By Chebyshev's Inequality

$P[|X-\mu| \geq k \sigma] \leq \dfrac{1}{k^2}$

$20 - 6 = 14 = 7\sigma$

$P[\text{errors}\geq 20] \leq \dfrac{1}{7^2} = \dfrac{1}{49}$