Advanced Monty Hall Problem with N door and M cars

From: Jack (mrjack_2005_at_yahoo.com)
Date: 02/21/05 

Date: Mon, 21 Feb 2005 13:29:37 +0000 (UTC)

Hello Everybody,
I really need you help in solving an advanced Monty hall problem.
Assuming that we have N door with M of these door have cars behind
them and N-M of these door has $1 bill behind them.
Assuming that the player made an initial selection (she picked a door
D1), now.... Monty open a door that has a $1 bill behind .... now he
asks her, if she want to stay with her initial choice or if she wants
to switch?

What is the probability of winning if she stay with her choice? Isn't
it P(winning if she stay with her inital decision) = M/N?

What is the probability of winning a car if she switched to different
door?

Thanks
Jack

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