# Statistics question about particle hitting a detector and chance of detection

This is a statistics problem which i need some help with as amu unsure how to answer it.

Particles hitting a detector undergo a collision after an average path length Lo= 10 cm. After the collision, the particle deposits all of its energy in thedetector and is stopped. How thick does the detector need to be so that 99%of the incoming particles are stopped?

I believe that using a poisson distribution may help but tried using the poisson distribution and couldn't get a reasonable answer.

Any help or tips would be appreciated.

In the simple model of the situation that I'm sure you're using, the path length will not be Poisson-distributed, but rather exponentially distributed (it is the interevent time of a Poisson process, not the number of events). So you want to compute the 99th percentile of the exponential distribution with mean $10.$ Recall that if $X$ has that distribution, we have $$P(X\ge x) = e^{-x/10},$$ so just set $0.01 = e^{-x/10}$ and solve.