Congrats janyne too all the college entrants! I can't even imagine!!!!

Well DS8.5 surprised me tonight. I was quite impressed with his reasoning even though he didn't get it exactly right. Perhaps most 8yr olds would get this but I was impressed. blush

This is from Zaccaro's Math book but I used my own numbers b/c I didn't feel like getting the book out.

I said "THere are 10 doors and a prize behind one of the doors. What are the odds of picking the right door?"
he said, "1 in 10."
I said, "So the host opens all the doors except #8 (your choice) and #1." (he doesn't open either door). What is the odd of door #1 being the one?
he said, "1 in 2"
I said, "What is the odd of door #8 being the correct one?" - here's where he shocked me.
He said, "1 in 10." (he got that the odds didn't change for his choice. And we've not done any probability beyond flipping coins).
I said, "Do you stay with your choice or choose door #1?"
He said, "Well the host doesn't want to give me the prize and wants to trick me into changing."
I said, "Don't go on emotion, just look at the numbers."
He said, "I'd stay with door #8."

At this point he smiled and said, "No, I'd choose door #1. That was is 1 in 2 chances of being it."

Now it's really 9 in 10 chance for door #1 but he got that the odds for door 1 was different from door 2, and that the odds for door 2 hadn't changed w/ all the others being opened.

Here's what Zaccaro says:
Zaccaro did the problem w/ just 3 doors rather than 10.

"this problem is so counter-intuitive that some of the smartest people in the world not only answer incorrectly that the contestant's chances are 1 in 2 for both doors, but they refuse to believe the correct answer when they hear it. The correct answer is that if the contestant keeps her original door, her chances of winning are 1 in 3. If she switches doors, her chances of winning would be 2 in 3." (not in 1 in 3). So she has double the chance of winning if she switches.