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Callifo Forums Junkie Location: Gawler, SA Registered: August 2003	Re: THE STUPIDEST RIDDLE EVER!! Tue, 30 August 2005 07:44 After finding the proper maths behind it, I have to admit it, we are wrong. Quote: P[A|B] = Pr[A and B]/P[B] Take a typical situation in the game. Suppose the contestant has chosen Door 3 and Monty Hall reveals that there is a goat behind Door 2. Let us compute the conditional probability that the car is behind Door 1. Let A stand for the condition that there is a car behind Door 1 and the contestant has chosen Door 3. Let B stand for the condition that Monty Hall has revealed that there is a goat behind Door 2 given that the contestant has chosen Door 3. The probability of A and B ( P[A and B] ) is just (1/3)(1/3)=1/9 because if the car is behind Door 1 and the contestant has chosen Door 3 it is 100 percent certain that Monty Hall will show what is behind Door 2. The problem is the computation of the probability of being shown a goat behind Door 2 given that the choice was Door 3. This situation can arise in two ways. One, when the car is behind Door 1 and another when the car is behind Door 3. The first way has a probability of 1/9, as has already been computed above. In the second way, the host could reveal either what is behind Door 1 or Door 2. If he is equally likely to choose either of these doors then the prob ability of the second way is (1/2)(1/9). Therefore the probabil ity of there being revealed a goat behind Door 2 when the con testant has chosen Door 3 is (1/9) + (1/2)(1/9) = (3/2)(1/9). This is the probability of B; i.e., P[B]. The conditional probability we want, P[A|B], is given by P[A|B] = P[A and B]/P[B] = (l/9)/(3/2)(1/9) = 2/3. This means that the conditional probability that the car is behind Door 3 given that the contestant has chosen Door 3 and has been shown that there is a goat behind Door 2 is only l/3. Therefore it is worthwhile to switch. This other conditional probability can be calculated either as 1 - P[A|B], or from the probability the car is behind Door 3 given that the contestant has chosen Door 3 and has been shown a goat behind Door 2. This latter probability is (1/3)(1/3)(1/2) so when it divided by P[B] one gets l/3. [Report message to a moderator]

	Subject	Poster	Date
	THE STUPIDEST RIDDLE EVER!!	xolent	Sun, 28 August 2005 14:47
	Re: THE STUPIDEST RIDDLE EVER!!	ae86drift	Sun, 28 August 2005 15:06
	Re: THE STUPIDEST RIDDLE EVER!!	tyottsoarer	Sun, 28 August 2005 15:09
	Re: THE STUPIDEST RIDDLE EVER!!	ShiRi	Sun, 28 August 2005 15:12
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Sun, 28 August 2005 23:15
	Re: THE STUPIDEST RIDDLE EVER!!	BabyZ	Sun, 28 August 2005 23:45
	Re: THE STUPIDEST RIDDLE EVER!!	Callifo	Mon, 29 August 2005 02:17
	Re: THE STUPIDEST RIDDLE EVER!!	-gt-	Mon, 29 August 2005 02:33
	Re: THE STUPIDEST RIDDLE EVER!!	ShiRi	Sun, 28 August 2005 15:20
	Re: THE STUPIDEST RIDDLE EVER!!	mc68	Sun, 28 August 2005 15:24
	Re: THE STUPIDEST RIDDLE EVER!!	tyottsoarer	Sun, 28 August 2005 15:32
	Re: THE STUPIDEST RIDDLE EVER!!	ae86drift	Sun, 28 August 2005 17:42
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Sun, 28 August 2005 23:51
	Re: THE STUPIDEST RIDDLE EVER!!	xolent	Mon, 29 August 2005 01:17
	Re: THE STUPIDEST RIDDLE EVER!!	draven	Mon, 29 August 2005 01:30
	Re: THE STUPIDEST RIDDLE EVER!!	RWDboy	Mon, 29 August 2005 02:25
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Mon, 29 August 2005 02:25
	Re: THE STUPIDEST RIDDLE EVER!!	BabyZ	Mon, 29 August 2005 02:38
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Mon, 29 August 2005 02:40
	Re: THE STUPIDEST RIDDLE EVER!!	Callifo	Mon, 29 August 2005 02:51
	Re: THE STUPIDEST RIDDLE EVER!!	RWDboy	Mon, 29 August 2005 02:41
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Mon, 29 August 2005 02:54
	Re: THE STUPIDEST RIDDLE EVER!!	rthy	Mon, 29 August 2005 02:58
	Re: THE STUPIDEST RIDDLE EVER!!	-gt-	Mon, 29 August 2005 03:04
	Re: THE STUPIDEST RIDDLE EVER!!	rthy	Mon, 29 August 2005 03:16
	Re: THE STUPIDEST RIDDLE EVER!!	ndgcpr	Mon, 29 August 2005 22:52
	Re: THE STUPIDEST RIDDLE EVER!!	RWDboy	Mon, 29 August 2005 03:22
	Re: THE STUPIDEST RIDDLE EVER!!	RWDboy	Mon, 29 August 2005 03:36
	Re: THE STUPIDEST RIDDLE EVER!!	Caledwvech	Mon, 29 August 2005 09:52
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Mon, 29 August 2005 10:00
	Re: THE STUPIDEST RIDDLE EVER!!	CrUZsida	Tue, 30 August 2005 01:26
	Re: THE STUPIDEST RIDDLE EVER!!	Squid	Tue, 30 August 2005 02:25
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Tue, 30 August 2005 02:31
	Re: THE STUPIDEST RIDDLE EVER!!	Squid	Tue, 30 August 2005 02:43
	Re: THE STUPIDEST RIDDLE EVER!!	CrUZsida	Tue, 30 August 2005 02:32
	Re: THE STUPIDEST RIDDLE EVER!!	Squid	Tue, 30 August 2005 02:38
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Tue, 30 August 2005 02:41
	Re: THE STUPIDEST RIDDLE EVER!!	CrUZsida	Tue, 30 August 2005 02:57
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Tue, 30 August 2005 03:01
	Re: THE STUPIDEST RIDDLE EVER!!	CrUZsida	Tue, 30 August 2005 03:12
	Re: THE STUPIDEST RIDDLE EVER!!	draven	Tue, 30 August 2005 03:05
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Tue, 30 August 2005 03:11
	Re: THE STUPIDEST RIDDLE EVER!!	Shraka	Tue, 30 August 2005 03:50
	Re: THE STUPIDEST RIDDLE EVER!!	RWDboy	Tue, 30 August 2005 03:55
	Re: THE STUPIDEST RIDDLE EVER!!	CrUZsida	Tue, 30 August 2005 04:19
	Re: THE STUPIDEST RIDDLE EVER!!	SupraPete	Tue, 30 August 2005 04:02
	Re: THE STUPIDEST RIDDLE EVER!!	SupraPete	Tue, 30 August 2005 04:39
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Tue, 30 August 2005 04:43
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Tue, 30 August 2005 04:47
	Re: THE STUPIDEST RIDDLE EVER!!	SupraPete	Tue, 30 August 2005 04:50
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Tue, 30 August 2005 04:53
	Re: THE STUPIDEST RIDDLE EVER!!	white86	Tue, 30 August 2005 05:44
	Re: THE STUPIDEST RIDDLE EVER!!	SupraPete	Tue, 30 August 2005 06:35
	Re: THE STUPIDEST RIDDLE EVER!!	Squid	Tue, 30 August 2005 23:45
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Tue, 30 August 2005 05:50
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Tue, 30 August 2005 06:46
	Re: THE STUPIDEST RIDDLE EVER!!	Callifo	Tue, 30 August 2005 07:02
	Re: THE STUPIDEST RIDDLE EVER!!	SupraPete	Tue, 30 August 2005 07:04
	Re: THE STUPIDEST RIDDLE EVER!!	BabyZ	Tue, 30 August 2005 07:39
	Re: THE STUPIDEST RIDDLE EVER!!	Callifo	Tue, 30 August 2005 07:44
	Re: THE STUPIDEST RIDDLE EVER!!	Shraka	Tue, 30 August 2005 13:20
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Tue, 30 August 2005 13:30
	Re: THE STUPIDEST RIDDLE EVER!!	Shraka	Tue, 30 August 2005 13:49
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Tue, 30 August 2005 14:01
	Re: THE STUPIDEST RIDDLE EVER!!	SupraPete	Tue, 30 August 2005 14:03
	Re: THE STUPIDEST RIDDLE EVER!!	Shraka	Tue, 30 August 2005 14:07
	Re: THE STUPIDEST RIDDLE EVER!!	CrUZsida	Wed, 31 August 2005 01:05
	Re: THE STUPIDEST RIDDLE EVER!!	SupraPete	Wed, 31 August 2005 01:14
	Re: THE STUPIDEST RIDDLE EVER!!	CrUZsida	Wed, 31 August 2005 01:19
	Re: THE STUPIDEST RIDDLE EVER!!	SupraPete	Wed, 31 August 2005 01:27
	Re: THE STUPIDEST RIDDLE EVER!!	CrUZsida	Wed, 31 August 2005 01:45
	Re: THE STUPIDEST RIDDLE EVER!!	SupraPete	Wed, 31 August 2005 01:47
	Re: THE STUPIDEST RIDDLE EVER!!	SupraPete	Wed, 31 August 2005 02:03
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Wed, 31 August 2005 14:29
	Re: THE STUPIDEST RIDDLE EVER!!	SupraPete	Thu, 01 September 2005 04:40
	Re: THE STUPIDEST RIDDLE EVER!!	Shraka	Thu, 01 September 2005 05:06
	Re: THE STUPIDEST RIDDLE EVER!!	poh_86	Fri, 02 September 2005 09:53
	Re: THE STUPIDEST RIDDLE EVER!!	mynameisrodney	Fri, 02 September 2005 10:11
	Re: THE STUPIDEST RIDDLE EVER!!	CrUZsida	Fri, 02 September 2005 10:15
	Re: THE STUPIDEST RIDDLE EVER!!	trevtrev	Mon, 05 September 2005 03:14
	Re: THE STUPIDEST RIDDLE EVER!!	CrUZsida	Mon, 05 September 2005 03:22

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