Computer screen and Poisson approximation

Question

I am struggling with a elementary probability exercice which I don't see how to "translate" it.

I have a computer screen with resolution $768\times1024$ pixels. We suppose that pixels are independent and such that the probability that a pixel is unusable is $\frac{9}{10^7}.$

1. What is the distribution of the number $X$ of unusable pixels ?
2. If there is $3$ unusable pixels then the screen is unsaleable. Compute an approximation of the probability that a screen is indeed unsaleable.

My idea was to consider that each pixel is view as a random variable $Y$ with Bernoulli distribution with parameters $p=\frac{9}{10^7}.$

So that $X$ is a binomial with parameter $(768\times1024,\frac{9}{10^7}).$

To answer $2$ pretty sure we need to use a Poisson approximation. But not sure about my answer to $1.$

Answer 1

I agree with your answer to (1).

For (2), I think Poisson approximation is fine. Having said that, using a hand-held calculator, I was able to get a good result using the binomial distribution directly.