Author Topic: Final Decision (Read 8689 times)

MANDO · « **Reply #105 on:** December 05, 2004, 12:05:51 PM »

lasersailor, no, I cant confirm that, you are wrong

He should not drop a "random" bomb. But you have an interesting idea.

Just after losing the "training" bomb, and with the determined decission to change the lever before the attack, he can just drop the bomb CURRENTLY SELECTED (not a random one), he has 33% chances that this is a real bomb. If it is real, he can RTB without risking into the enemy ack.

You have, indirectly, optimized the solution, WTG

ccvi · « **Reply #106 on:** December 05, 2004, 01:35:42 PM »

Quote

Originally posted by BlauK
If you lose a real bomb, you can disregard those cases, because they do not fulfill the stated case.

That's correct. But this is not what mandos solution (a solution to a different problem) is doing.

MANDO · « **Reply #107 on:** December 05, 2004, 01:40:05 PM »

ccvi, you are describing a different problem, not me. Knowing that single case, losing the real bomb has the very same probabilities than the pilot losing his left leg.

ccvi · « **Reply #108 on:** December 05, 2004, 01:50:41 PM »

And the same probability as losing an unselected dud.

MANDO · « **Reply #109 on:** December 05, 2004, 02:05:23 PM »

Quote

Originally posted by ccvi
And the same probability as losing an unselected dud.

You dont know whether or not the remaining dud was unselected.

ccvi · « **Reply #110 on:** December 05, 2004, 02:25:17 PM »

At the moment of drop it's also unknown whether the lost bomb was real or a training one.

Using quotes from the initial post, please explain why you think that
- the probability of losing a selected bomb is 0.
- the probability of losing a real bomb is 0.

lasersailor184 · « **Reply #111 on:** December 05, 2004, 03:24:00 PM »

Vorticon, I thought the exact same thing initially. But training bombs are made out of all metal to weigh the exact same.

However mando, I'm still right. It's the only solution there is with decreasing risk for nothing.

vorticon · « **Reply #112 on:** December 05, 2004, 03:34:34 PM »

Quote

Originally posted by lasersailor184
Vorticon, I thought the exact same thing initially. But training bombs are made out of all metal to weigh the exact same.

However mando, I'm still right. It's the only solution there is with decreasing risk for nothing.

ah...in which case, you response is the only acceptable course of action...unless he has a wingman.

MANDO · « **Reply #113 on:** December 05, 2004, 04:48:31 PM »

Quote

Originally posted by lasersailor184
However mando, I'm still right. It's the only solution there is with decreasing risk for nothing.

But not droping a bomb randomly, just drop the selected bomb.

MANDO · « **Reply #114 on:** December 05, 2004, 04:54:02 PM »

Quote

Originally posted by ccvi
At the moment of drop it's also unknown whether the lost bomb was real or a training one.

Using quotes from the initial post, please explain why you think that
- the probability of losing a selected bomb is 0.
- the probability of losing a real bomb is 0.

It is unknown by the pilot, but the lost bomb was RED, and the pilot was aware of that few seconds later.

If selected bomb is lost, the pilot is forced to move the lever. So, the solution does not change "move the lever".

The probability of losing real bombs is 0, because the only lost one is RED. Remember, for TWO red, you lost ONE, for one green, you lost CERO, for one pilot head, you lost 0, etc. Only 1 RED bomb failed, you cannot from a single case assume the green bomb will fail also (or the left leg or the pilot).

lasersailor184 · « **Reply #115 on:** December 05, 2004, 05:28:52 PM »

It is unknown which bomb is on which rack. Therefor, it doesn't matter if you switch the lever or not. You drop a bomb. If it explodes you RTB. If it doesn't you go on to target.

BlauK · « **Reply #116 on:** December 05, 2004, 05:31:29 PM »

Originally posted by ccvi
Using quotes from the initial post, please explain why you think that
- the probability of losing a selected bomb is 0.
- the probability of losing a real bomb is 0.

---

Quoting the original text:
"This lever was at the lower position, so left pilon was selected."
" As he was aproaching the target, the center pilon led switched off, by some mechanical problem that bomb was released."

Left one was selected, center one was lost. Therefore this question does not deal with losing a selected bomb!

Quote:
"The pilot inverted the plane quickly and looking at his high six saw a bright red object descending. He was lucky, it was one of the two training bombs."

Like you see again, it was the training bomb hat was lost.

Only now comes the question about switching and its probabilities in tis particular case.....

Mando's program takes a bit wider view though. It allows also other initial selections and training bomb losses also from other positions than center. The described case falls under the same category though, since it is just describing one of the cases.

ccvi,
to me it seems that you want to change the question as: "What is the probability that a pilot with these three bombs in unknown positions would lose any one of the bombs, recognize it, and then think of switching the selection or not?"

That is not the original question though.

MANDO · « **Reply #117 on:** December 05, 2004, 06:15:19 PM »

Quote

Originally posted by lasersailor184
It is unknown which bomb is on which rack. Therefor, it doesn't matter if you switch the lever or not. You drop a bomb. If it explodes you RTB. If it doesn't you go on to target.

lasersailor184, to make it simpler, the chances to have the lever where the real bomb is from the very beginning are 1/3. So, there are 2/3 that the real bomb is on the other group of racks. One of the other racks is empty now, you lost one training bomb, so, you still have 2/3 chances of having the real bomb on the other rack. If you want to drop a bomb and see what happens, drop the one currently selected, but ONLY if you have the determined decission of changing the lever at the moment of the attack.

lasersailor184 · « **Reply #118 on:** December 05, 2004, 09:45:39 PM »

You are overlooking the simplicity of this problem, as is everyone who is trying to quote difficult statistics.

The real bomb is either on the left pilon, or the right pilon. You do not know, nor can any statician justifiy that there is more than a 50% chance whether or not you have the real bomb selected.

Next, factor in that the pilot will be flying through a heavily defended area. Does he want to go in there with a chance of him being killed to drop a practice bomb and do nothing? **** no!

So my solution still stands except for another which I'll touch upon in a minute. He picks one pylon **DOESN'T MATTER WHICH BECAUSE THE CHANCES ARE THE SAME.** He drops it over open ground and watches the effect. If he has a real bomb left, then it's worth the chance to fly into the defended area. If he doesn't he flies home because the result isn't worth the risk.

BlauK · « **Reply #119 on:** December 06, 2004, 04:39:13 AM »

laser,

read the links to Monty Hall scenario or search the web for it. Then tell us whu the mathematicians and statisticians cannot prove it wrong!

You yourself are not considering the fact that the whole case is not the same as making a selection between 2 options.. it is about switching th eoriginal selection or not switching. And that makes the difference, believe it or not!

The question here is simply about to switch or not to switch. Solutions like.. fly over friendly base to identify the bombs.. are very nice work-arounds, but they do not tackle the actual question of probabilities.