Spoiler for hint

Let's say the scenario were a little different.

After Jennifer picks Door #2, Monty Barker does not open Door #1. Instead, he decides to be generous and offer Jennifer to trade what is behind Door #2 for what is behind both Door #1 and Door #3.

Assuming that Monty is not intentionally trying to entice Jennifer away from Door #2, it obviously makes sense to trade.

The odds of the Jaguar XJS being behind Door #2 are one in three.

The odds of the Jaguar XJS being behind either Door #1 or Door #3 are two in three.

Jennifer knows she will get at least one goat if she trades, but she also doubles her chances of getting the car.

Now, back in the real scenario, it does not matter that Monty shows Jennifer the Goat behind Door #1. We already knew there was a goat behind at least one of the remaining doors. Switching still doubles her chances of getting the car. The goat behind Door #1 has just been discarded before she wins it, instead of afterwards.

After Jennifer picks Door #2, Monty Barker does not open Door #1. Instead, he decides to be generous and offer Jennifer to trade what is behind Door #2 for what is behind both Door #1 and Door #3.

Assuming that Monty is not intentionally trying to entice Jennifer away from Door #2, it obviously makes sense to trade.

The odds of the Jaguar XJS being behind Door #2 are one in three.

The odds of the Jaguar XJS being behind either Door #1 or Door #3 are two in three.

Jennifer knows she will get at least one goat if she trades, but she also doubles her chances of getting the car.

Now, back in the real scenario, it does not matter that Monty shows Jennifer the Goat behind Door #1. We already knew there was a goat behind at least one of the remaining doors. Switching still doubles her chances of getting the car. The goat behind Door #1 has just been discarded before she wins it, instead of afterwards.

Spoiler for hint

If the above still does not convince you, then maybe this one will. This is the method my friend used to convince me after I argued with him for quite a while about it.

Change the scenario from three doors to a hundred boxes.

Now, there are one hundred boxes to pick from. One has a key to the fabulous Jaguar XJS, the other ninety-nine are actually boxes of Kleenex.

After Jennifer picks box #54, Monty opens all of the other boxes, except #43, to show that they are all tissues.

Finally, he offers Jennifer a chance to trade her box for #43.

Should she make the trade or keep the box she has.

It should be obvious at this extreme that there is still only a one percent chance of box #54 having the key, but a ninety-nine percent chance that #43 has the key.

Change the scenario from three doors to a hundred boxes.

Now, there are one hundred boxes to pick from. One has a key to the fabulous Jaguar XJS, the other ninety-nine are actually boxes of Kleenex.

After Jennifer picks box #54, Monty opens all of the other boxes, except #43, to show that they are all tissues.

Finally, he offers Jennifer a chance to trade her box for #43.

Should she make the trade or keep the box she has.

It should be obvious at this extreme that there is still only a one percent chance of box #54 having the key, but a ninety-nine percent chance that #43 has the key.