Author Topic: Final Decision (Read 7359 times)

MANDO · « **Reply #90 on:** December 03, 2004, 09:22:15 AM »

Quote

Originally posted by BlauK
If the selected bomb is lost, then

then you also NEED to change the lever. The question was, what should do the pilot?

CHANGE THE LEVER ALWAYS.

dedalos · « **Reply #91 on:** December 03, 2004, 09:49:51 AM »

It is 50/50. The formula used to calculate the probability that gives the 2/3 is the other bomb/door, is based on knowing that the bomb is red before droping it.

http://astro.uchicago.edu/rranch/vkashyap/Misc/mh.html

__________________

nazgulAX · « **Reply #92 on:** December 03, 2004, 09:56:40 AM »

select the left pilon

BlauK · « **Reply #93 on:** December 03, 2004, 01:12:48 PM »

Mando,
If he does not switch in such case when the selected bomb is lost, there is no point to attack at all! I agree with your earlier case, but now you are mixing things. The Monty Hall scenarion does not include a case where the selected door (with a goat) is opened and then a new selection is made. Then the question would not be "to switch or not?" anymore, but "where to switch?"

BlauK · « **Reply #94 on:** December 03, 2004, 01:19:46 PM »

dedalos,
where in the formulas is that "knowing before opening" indicated?

IMO, the condition is that "an unselected door with a goat IS/WAS opened". It is exactly the same as "an unselected red bomb was lost"

That is the situation you are in now. What are the success probabilities of keeping and switching?

TEShaw · « **Reply #95 on:** December 03, 2004, 02:54:10 PM »

I'm enjoying this debate and the articulate way you guys are putting forth your arguments.

However, if Monte Hall is God, then MANDO's argument is irrefutable.

regards,

Airman T. E. Shaw

lasersailor184 · « **Reply #96 on:** December 03, 2004, 03:58:58 PM »

Umm guys, you are making this way way too difficult. It doesn't take a member of Mensa to figure it out (but don't worry, I'm here to solve it for you).

On the way to the target the guy finds a clear open space and drops a random bomb. Doesn't matter which one.

One of two things can happen:

1.) The bomb will impact with the ground, but not explode. Hence the pilot just dropped the practice bomb. If this happens, he continues with the mission.

2.) The bomb will impact with the ground and detonate. Hence the pilot just dropped the real bomb. If this happens, there is no use risking his life and the plane to drop a practice bomb that won't do anything anyway. If the pilot dropped the real bomb, then he just flies home and chalks the day up as a loss.

HOTDAMN! I'm good.

dedalos · « **Reply #97 on:** December 03, 2004, 04:12:15 PM »

Quote

Originally posted by BlauK
dedalos,
where in the formulas is that "knowing before opening" indicated?

IMO, the condition is that "an unselected door with a goat IS/WAS opened". It is exactly the same as "an unselected red bomb was lost"

That is the situation you are in now. What are the success probabilities of keeping and switching?

I bolded the part that to me means knowing before opening (He is not going to open the one witht he price). This is how I understand it atlist.

The a priori probability that the prize is behind door X, P(X) = 1/3

The probability that Monty Hall opens door B if the prize were behind A,
P(Monty opens B|A) = 1/2

The probability that Monty Hall opens door B if the prize were behind B,
P(Monty opens B|B) = 0

The probability that Monty Hall opens door B if the prize were behind C,
P(Monty opens B|C) = 1

The probability that Month Hall opens door B is then
p(Monty opens B) = p(A)*p(M.o. B|A) + p(B)*p(M.o. B|B) + p(C)*p(M.o. B|C)
       = 1/6 + 0 + 1/3 = 1/2

Then, by Bayes' Theorem,

P(A|Monty opens B) = p(A)*p(Monty opens B|A)/p(Monty opens B)
       = (1/6)/(1/2)
       = 1/3
and
P(C|Monty opens B) = p(C)*p(Monty opens B|C)/p(Monty opens B)
       = (1/3)/(1/2)
       = 2/3

So, since th ebomb is droped accidently this does not apply and the prob now is 50/50

lasersailor184 · « **Reply #98 on:** December 04, 2004, 10:52:31 AM »

I'm sorry, did I ruin it for everyone?

BlauK · « **Reply #99 on:** December 04, 2004, 10:57:44 AM »

dedalos,
ok... show me the formula all the way from the beginning with an accidentally lost training bomb. If you lose a real bomb, you can disregard those cases, because they do not fulfill the stated case.

How will you end up with 50:50 for switching case?

What is your bases for the statement that this does not apply for an accidentally lost bomb (which WAS already lost and therefore happens in 100% of the possible relevant cases!!!)

yuto · « **Reply #100 on:** December 04, 2004, 02:26:36 PM »

So you play paper/rock/scissors with a robot which you are told is completely random.

First try:
you - rock
robot - paper

Second try:
you - rock
robot - paper

Third try:
you - rock
robot - paper

. . . .(continues for 10 minutes)

On the 101st try,
- a mathematician/statistician would stick with his rock
- a guy with some sense would go with scissors

DieAz · « **Reply #101 on:** December 04, 2004, 09:15:53 PM »

Quote

Originally posted by yuto
So you play paper/rock/scissors with a robot which you are told is completely random.

First try:
you - rock
robot - paper

Second try:
you - rock
robot - paper

Third try:
you - rock
robot - paper

. . . .(continues for 10 minutes)

On the 101st try,
- a mathematician/statistician would stick with his rock
- a guy with some sense would go with scissors

and get pounded by a rock

MANDO · « **Reply #102 on:** December 05, 2004, 05:13:50 AM »

Quote

Originally posted by BlauK
Mando,
If he does not switch in such case when the selected bomb is lost, there is no point to attack at all!

BlauK, in this case he needs to switch (is "forced" to switch by the circumstances). We can consider that, for this case in particular, "to switch" is not a decission, the decission for this case is "where to switch" with only 1/2 of success.

So, when the pilot may switch, he "should" switch. When the pilot is forced to switch, he will switch.

lasersailor184 · « **Reply #103 on:** December 05, 2004, 11:51:59 AM »

Mando, can you confirm that I'm right?

vorticon · « **Reply #104 on:** December 05, 2004, 11:58:17 AM »

hmm, couldnt the pilot do a roll to see wich side is "heavier" (im assuming training bombs are lighter...not sure if thats correct) then switch to that side?