Barstow Community College Probability in the Monty Hall Dilemma Discussion

I’m working on a probability question and need an explanation to help me study.

he Monty Hall ProblemTheMonty Hall Problemis a famous probability puzzle, based on thetelevision game showLet’s Make a Deal.It has been formulated as follows:“Suppose you’re on a game show, and you’re given the choice of three doors: Behind onedoor is a car; behind the others, goats. You pick a door, say No. 1, and the host, whoknows what’s behind the doors, opens another door, say No. 3, which has a goat. He thensays to you, ‘Do you want to pick door No. 2?’ Is it to your advantage to switch yourchoice?” (From Parade magazine’s Ask Marilyn column)It turns out that you should indeed switch your choice to increase your chance of winning, which mightseem counter-intuitive at first glance.