Given $n$ people, each has probability $v$ of having a virus. Of those with the virus, they are hospitalized with probability $p$. Independently of having the virus, any of the $n$ people may be hospitalized for a different reason with probability $a$.
Let $X$ be a random variable that denotes the number of the $n$ people who are hospitalized, and $Y$ be a random variable that denotes the number of people in the hospital that have the virus.
Find the distributions of X and Y.
I think this situation reflects a certain distribution. I was thinking Bernoulli, but I can't seem to think of a way to represent both of the random variables. Can anyone help with this please?