This seems identical to the Monty Hall problem, except that the typical telling of the Monty Hall problem elides an important detail: that Monty knows which door conceals the car and intentionally always picks one that conceals a goat.
With that omitted (on Wikipedia [0], it's omitted in both the introduction to the page and the "canonical" reader's letter it quotes), people correctly conclude that their chance of winning doesn't go up by switching doors.
With that omitted (on Wikipedia [0], it's omitted in both the introduction to the page and the "canonical" reader's letter it quotes), people correctly conclude that their chance of winning doesn't go up by switching doors.
[0] https://en.m.wikipedia.org/wiki/Monty_Hall_problem