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```
>>> 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

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

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

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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