easy Probability
A release-checked easy problem for training Poisson, Law of Total Probability, Conditional Distributions, Conditional Probability.
You are a winner of a lottery! However, you may not be the only winner. The number of other people who won the lottery is $N \sim \text{Poisson}(\lambda)$, where $\lambda > 0$ is a constant. Given $N = n$, the person who actually receives all the money is randomly selected from the $n+1$ total winners (you and the other $n$ people). Find the probability that you actually receive the money when $\lambda = 1$, rounded to the nearest thousandth.
This Probability problem is tagged Poisson, Law of Total Probability, Conditional Distributions, Conditional Probability. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
Probability · Akuna
Probability
Probability
Probability · SIG, DE Shaw
Probability · SIG, Jane Street
Probability · Jane Street