The movie 21 Please explain the math.

[Sly]

It appears there are a few engineers with some math background on this forum that are able to explain this math problem to me shown in the movie 21.

Here is the problem as shown in the movie.

There are three doors, one door has a car, the other two doors have goats. The contestant wants to win the car.

The contestant chooses door number 1. The game show host opens door number 3 which is a goat not a car.

The game show host than asks the contestant if he would like to change his pick from door #1 to door #2.

The contestant does decide to change from door number 1 to door #2. He states by changing from original chosen door #1 to door #2 his odds of winning the car increased to 66.7%.

I do not understand how the odds went from 50/50 to 66.7%. If he wants to win the car, it is either behind door 1 or door 2, 50/50 odds?

What am I missing. Did you see the movie.

[Eugene]

I did not see the movie, but there are two possibilities and the answer depends on which one is the case.
1) The host opens one of two remaining doors at random. In this case your logic is correct – odds remain 50/50.
2) The host knows which door has a car behind it, and he intentionally opens the one which does NOT have a car. In this case it’s better to switch.

[Eugene]

I did not see the movie, but there are two possibilities and the answer depends on which one is the case.
1) The host opens one of two remaining doors at random. In this case your logic is correct – odds remain 50/50.
2) The host knows which door has a car behind it, and he intentionally opens the one which does NOT have a car. In this case it’s better to switch.

[Eugene]

I did not see the movie, but there are two possibilities and the answer depends on which one is the case.
1) The host opens one of two remaining doors at random. In this case your logic is correct – odds remain 50/50.
2) The host knows which door has a car behind it, and he intentionally opens the one which does NOT have a car. In this case it’s better to switch.

[Eugene]

I did not see the movie, but there are two possibilities and the answer depends on which one is the case.
1) The host opens one of two remaining doors at random. In this case your logic is correct – odds remain 50/50.
2) The host knows which door has a car behind it, and he intentionally opens the one which does NOT have a car. In this case it’s better to switch.

[Eugene]

I did not see the movie, but there are two possibilities and the answer depends on which one is the case.
1) The host opens one of two remaining doors at random. In this case your logic is correct – odds remain 50/50.
2) The host knows which door has a car behind it, and he intentionally opens the one which does NOT have a car. In this case it’s better to switch.

[bsrsharma]

The host knows which door has a car behind it

Then switching doors will change odds to 1 i.e. certainty and not 2/3.

[bsrsharma]

The host knows which door has a car behind it

Then switching doors will change odds to 1 i.e. certainty and not 2/3.

[bsrsharma]

The host knows which door has a car behind it

Then switching doors will change odds to 1 i.e. certainty and not 2/3.

[bsrsharma]

The host knows which door has a car behind it

Then switching doors will change odds to 1 i.e. certainty and not 2/3.

[bsrsharma]

The host knows which door has a car behind it

Then switching doors will change odds to 1 i.e. certainty and not 2/3.

[Eugene]

No, because it’s possible that the car is behind the door that the player picked initially.

[Eugene]

No, because it’s possible that the car is behind the door that the player picked initially.

[Eugene]

No, because it’s possible that the car is behind the door that the player picked initially.

[Eugene]

No, because it’s possible that the car is behind the door that the player picked initially.

[Author]

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