I'm not entirely sure how to go about solving this problem.
At first glance I thought W was obviously the minimum, as the mean is 1. However, $Pr(W < 2 ) e^{-1}*(1 +1) = .7357$, which is not one of the available options.
Any help would be much appreciated.
Use the fact that $W, X, Y$ are independent so that \begin{align} & P[\min(W, X, Y) \leq 2] = 1 - P[\min(W, X, Y) > 2] \\ = & 1 - P[W > 2, X > 2, Y > 2] \\ = & 1 - P[W > 2]P[X > 2]P[Y > 2]. \end{align} Now apply the Poisson distribution law for each probability, can you take it from here?