r3vbr
10-26-2004, 08:27 PM
At a TV show, there are "n" number of doors. Behind 1 of those doors there is a prize, and behind all other doors there is no prize.
The Show host asks for a guest to chose a door. So the guest choses a door but does not open it. The host (wich knows where the prize is) opens one of the doors that haven't been picked yet and opens it, revieling that there is no prize. The guest then choses another door, and the same procedure repeats itself, until only two doors are left, the one the guest choses and the one that is still remaining. So, still following the rule, he swiches to the remaining door and sees if he won or not.
1- What is the probability that the guest wins the prize? (present the formula the simplest way possible)
2- What is the probability when "n" (number of doors) is infinite? To write down the answer, use only the four basic operations and the number e (Euler = 2,71828...)
The Show host asks for a guest to chose a door. So the guest choses a door but does not open it. The host (wich knows where the prize is) opens one of the doors that haven't been picked yet and opens it, revieling that there is no prize. The guest then choses another door, and the same procedure repeats itself, until only two doors are left, the one the guest choses and the one that is still remaining. So, still following the rule, he swiches to the remaining door and sees if he won or not.
1- What is the probability that the guest wins the prize? (present the formula the simplest way possible)
2- What is the probability when "n" (number of doors) is infinite? To write down the answer, use only the four basic operations and the number e (Euler = 2,71828...)