While you are technically correct, it's implicitly stated ("game show") and correctly understood by the majority of readers. Take it from Marilyn vos Savant her

While you are technically correct, it's implicitly stated ("game show") and correctly understood by the majority of readers. Take it from Marilyn vos Savant herself: "Virtually all of my critics understood the intended scenario. I personally read nearly three thousand letters (out of the many additional thousands that arrived) and found nearly every one insisting simply that because two options remained (or an equivalent error), the chances were even. Very few raised questions about ambiguity, and the letters actually published in the column were not among those few." [0] The crux of the problem is the counter-intuitive nature of probabilities and information, possible choices and choices that could have been. It's a difficult problem, purported to have tripped up even Paul Erdős. [0] https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_behaviors https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_...