Probability question

Factual Questions
1

I was watching Deal or No Deal the other day. It was a special episode that offered 13 one million dollar cases, the left side of the board was the standard numbers. The contestant’s chances of picking a million dollar case at the start of the game was 50% (or 1 in 2).

Towards the end of the game there were 6 one million dollar cases left and two standard amounts. Howie proclaimed that the contestants had a 3 out of 4 chance of owning a one million case. Is this true or does the contestant’s chances still remain 50% that they had at the games start?

I suspect that this is somehow related to the Monte problem but I’m not sure. In the end, the contestants did not have a one million dollar case.

2

Howie is right. The probability doesn’t change in the Monty Hall problem because Monty knows what is behind each door, and will never reveal the prize.

In Let’s Make A Deal, the contestant has no knowledge of what’s in each briefcase, so the probabilities change every time they are opened.

3

Take it to the extreme. When there is only the contestant’s case left and there the only value remaining is one million dollars, the chances the contestant has the million dollar case must be 100%.