Headache generator
 

Exchanges with Nmap got me thinkin' about a puzzler.
Here goes:


There is a member of Mensa at a hotel.
His intelligence puts him right at the dividing line for membership (barely the top 2% of general population).

There are seven ballrooms occupied by people selected at random from the general population.

First, he enters ball room "G".
Including himself, there are 35 people in the room.

Second, he enters ball room "F".
Including himself, there are 40 people in the room.

Third, he enters ball room "E".
Including himself, there are 45 people in the room.

Fourth, he enters ball room "D".
Including himself, there are 50 people in the room.

Fifth, he enters ball room "C".
Including himself, there are 55 people in the room.

Sixth, he enters ball room "B".
Including himself, there are 60 people in the room.

Seventh, he enters ball room "A".
Including himself, there are 65 people in the room.


Question:
Upon entering which room did it become more likely than not (greater than 50% probability) that he was not the smartest person in the room?

D?

Extra credit:

There is a member of Mensa at a hotel.
His intelligence puts him right at the dividing line for membership (barely the top 2% of general population).

There are seven ballrooms occupied by people selected at random from the general population.

First, he enters ball room "G".
Excluding himself, there are 35 people in the room.

Second, he enters ball room "F".
Excluding himself, there are 40 people in the room.

Third, he enters ball room "E".
Excluding himself, there are 45 people in the room.

Fourth, he enters ball room "D".
Excluding himself, there are 50 people in the room.

Fifth, he enters ball room "C".
Excluding himself, there are 55 people in the room.

Sixth, he enters ball room "B".
Excluding himself, there are 60 people in the room.

Seventh, he enters ball room "A".
Excluding himself, there are 65 people in the room.


Question:
Upon entering which room did it become more likely than not (greater than 50% probability) that he was not the smartest person in the room?


<edit>
I'll leave these for awhile to see what the responses are.

In the case of "including himself" (34 others), the answer is room F.
(prob = 49.69% in room G, prob = 54.52% in room F, increasing thereafter)

In the case of "excluding himself" (35 others), the answer is room G.
(prob = 50.69% in room G, increasing thereafter)


How many were actually thinking rooms C, D, or E? :munchin

I had figured the probability per room before scrolling down to see your post with the answer. Upon coming to my answer of "G," I read the post with the correct answers, at which time my brain exploded.

I immediately blew it off altogether and started looking at other threads:boohoo

I for one enjoyed this pearl of honesty. Atta boy

Suppose it would've been simpler to ask:

1 - (.98^34) = ?
1 - (.98^35) = ?

But that's not any fun. :D