Re: Theory of Restricted Choice


ZipDoo wrote:
"Eric Kehr" <eric.kehr@xxxxxxxxxxxxx> wrote in message
news:IZydnWJ9wusyIhbZRVnyig@xxxxxxxxxxxx
bill wrote:
I wonder if the "Monty Hall" problem and the "Theory of Restricted
Choice" are similar
problems? regards

Bill

Another famous related probability question (actually a pair of questions)
is this:

Situation 1:
A family moves in next door. You ask the mother how many children she has
and she answers two. You then ask if she has at least one son and she says
yes. What is the probability that her other child is also a boy?

Situation 2:
A family moves in next door. You ask the mother how many children she has
and she answers two. Just then, a boy walks by and she says "Here's one of
them now". What is the probability that her other child is also a boy?

Eric Kehr

Those are nice examples, the answers to which are 1/3 and 1/2, respectively,
except possibly in China.

Actually, assuming equal numbers of boys and girls, the correct
probabilities are close to:

..3349 and .5175

varing slightly across the globe

Dave Flower



Even some eminent mathematicians have been tripped up by the Monty Hall
Problem. The list of victims even includes the Hungarian mathematician Paul
Erdos (see Paul Hoffman's biography of Erdos, "The Man Who Loved Only
Numbers," Hyperion, New York, 1988, pp. 233-238).

The best method I have found to convince a skeptic of the correct solution
to the Monty Hall Problem is to offer him an extreme example of the problem.
Take a standard deck of 52 cards, shuffle it thoroughly, and let the skeptic
pick one card from the deck at random and hold it, sight unseen. Then take
the remaining 51 cards, scan them without the skeptic seeing them, and then
show him 50 of those cards, none of which is the ace of spades. Set those
50 cards aside. You are now each holding one card. Ask him who is more
likely to be holding the ace of spades. If that doesn't convince him, reach
for your wallet.

Clay Waldrop

.

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