For each of the following modified monty hall scenarios, decide whether the contestant should switch doors or not. unless otherwise specified, monty, as in the original monty hall show, reveals a goat behind one door after the contestant has made their first choice. (a) there aren > 2 doors with 1 car andn-1 goats. (b) there are n > 2 doors with 1 car and n - 1 goats, but monty reveals n - 2 doors with goats behind them. (c) there aren > 2 doors with k < n - 1 cars and n - k goats, but monty reveals j