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#26 2013-10-25 20:23:43

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,833
Website

Re: Flaws in logic of solution to a couple of the logic problems

>>> import random
>>> def pickbag():
	bag = random.randrange(1,4)
	if bag == 1:
		return ['W','B'] #return a bag with a white and a black marble
	elif bag == 2:
		return ['W', 'W']
	else:
		return ['B', 'B']

	
>>> def pickmarble(bag):
	return random.choice(bag) #pick a random marble from the given bag

>>> def seeiftheothermarbleiswhite():
	bag = pickbag()
	marble = pickmarble(bag)
	if marble == 'W':
		if bag == ['W','W']:
			return True # First Marble AND second marble white
		else:
			return False # Only First Marble White
	else:
		return None #First marble is not white, aborting

Now, lets do the experiment 1 00 000 times and Mark the cases as Yes when the other marble are white, No when only the First marble is white, Other when the first is not white.

>>> Yes = 0
>>> No = 0
>>> Other = 0
>>> for i in xrange(100000):
	a = seeiftheothermarbleiswhite()
	if a:
		Yes += 1
	elif a == False:
		No += 1
	else:
		Other += 1

Now, since we are dealing only with cases when the first marble is white:

>>> Yes

33351
>>> No

16533
>>> Other

50116
>>> Yes/float(Yes + No)

0.6685710849170075

Now, that is very close to 2/3 and the rest is experimental error


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'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
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#27 2014-01-21 20:44:12

PalmerEldritch
Member
Registered: 2014-01-21
Posts: 1

Re: Flaws in logic of solution to a couple of the logic problems

ILIA wrote:

Let's say I originally picked door 1 then door 2 was opened showing the goat so we want to calculate probability of car behind door 1 given that door 2 has a goat and probability of car behind door 3 given that door 2 has a goat.

The flaw in your problem definition is the condition  "given that door 2 has a goat", it should be "given Monty opens Door 2"
.
If we call the 'probability that Monty opens Door 2', p(g2), then:
p(g2) = (1/3*1)  + (1/3 * 1/2)  + (1/3 * 0) = 1/2 and
p(g2)|(c1) = 1/2 and p(g2)|(c3) = 1

Plug those values into Bayes and you get 1/3 and 2/3

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