= Solution
The intended season calculation needs the additional assumption that scores in different games are <independent random variables>. The printed statement gives their common one-game distribution but does not explicitly state <independence>; identical marginals alone do not determine season probabilities.
Under <independence>, each game has <probability> $1-P(X=0)=1-e^{-\lambda}$ of at least one goal, so
$$
\boxed{P(\text{at least one goal in every game})=(1-e^{-\lambda})^{10}}.
$$
Without <independence> this product is not determined by the supplied marginal distribution.
Back to article page
