Kebab Roulette
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.
Mad Ade was partaking in a game of "Kebab Roulette", where a large cannon with six chambers, like those of a revolver, can contain ammunition. In Kebab Roulette, five of the chambers are left empty and one is filled with salad, the most hated thing of all time served kebab eaters. The idea is to spin the chamber and then stand in front of the cannon while someone fires it at you. If there is no loser, there is a second round, where another load of salad is added, so now two chambers contain salad and the cannon is fired twice. If you are lucky and get an empty chamber, you can eat your kebab saladfree; if you are unlucky and get the saladfilled chamber, you must eat all the salad before eating your kebab.
The cylinder containing the six chambers is spun before the first shot. But it may or may not be spun after putting in the salad and after taking the first shot.
Which of the following scenarios has the lowest probability of being saladfree, and what is the value as a percentage?
Spinning the cylinder after putting in the salad and spinning it again after the first shot.
Spinning the cylinder only after putting in the salad.
Spinning the cylinder only after firing the first shot.
Not spinning the cylinder either after putting in the salad or after taking the first shot.
The probability of staying saladfree on the first shot is the same in all the cases.
Remember the cannon has six chambers.
Answer
The second scenario has the lowest probability of remaining saladfree, i.e. 40%. The fourth scenario has the highest probability of staying saladfree, i.e. 50%.
Scenario I:
The probability of remaining saladfree in the first shot = 4/6 = 2/3.
Since the cylinder is spun after the first shot, the probability of nonsalad in the second shot = 4/6 = 2/3.
Hence, the probability of no salad in Scenario I = 2/3 * 2/3 = 4/9 = 44.44%.
Scenario II:
The probability of remaining saladfree in the first shot = 4/6 = 2/3.
Since the cylinder is spun after the first shot, the probability of nonsalad in the second shot = 3/5.
Hence, the probability of no salad in Scenario II = 2/3 * 3/5 = 2/5 = 40.00%.
Scenario III:
The probability of remaining saladfree in the first shot = 4/6 = 2/3.
Since the cylinder is spun after the first shot, the probability of nonsalad in the second shot = 4/6 = 2/3.
Hence, the probability of no salad in Scenario III = 2/3 * 2/3 = 4/9 = 44.44%.
Scenario IV:
The probability of remaining saladfree in the first shot = 4/6 = 2/3.
Since the cylinder is not spun after putting in the salad, both of the salads are in consecutive chambers. The probability of nonsalad in the second shot = 3/4.
Hence, the probability of no salad in Scenario IV = 2/3 * 3/4 = 1/2 = 50.00%.
Thus, the second scenario has the lowest probability of remaining saladfree, i.e. 40%. The fourth scenario has the highest probability of staying saladfree, i.e. 50%.
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Comments
Palsha
Apr 21, 2004
 Very tough, yet very good! 
jimbo
May 03, 2004
 This teaser is a complete mess. I can't even begin to suggest an edit. It clearly says that the chamber is spun before the first shot (but scenarios 3 and 4 contradict this). It says the canon is then fired twice. It should say the canon is fired a second time. There is no explanation of how the canon is "loaded". If one of the canon chambers can be loaded and then it is fired without being spun, can the newly loaded chamber be the one that is fired? This is not the case with a revolver which can only be loaded when the chamber is in a certain position, so that not all of the chambers are available for firing after it has been loaded.
Also, if one out of six chambers is loaded and the chambers are spun (as in two of the scenarios  plural) then the chances of being salad free are surely 5/6 not 4/6 as stated in the solution. I think this teaser needs a complete rewrite. 
krishnan
May 03, 2004
 I have to agree with Jimbo here. The wording is not clear and very confusing. 
madade
May 03, 2004
 I don't understand your confusion.
it states "In Kebab roulette five of the chambers are left empty and one is filled with salad, the most hated thing of all time served kebab eaters. The idea is to spin the chamber and then stand in front of the cannon while some one fires it at you."
which tells you that the cylinder is spun after the first load of salad in added. In all cases the cylinder with the chanber of salad is spun before the first shot, hence the same chance of remaining salad free on first shot of each scenario. The differences in renmaining salad free only apply after the second salad is added randomly, then you have the options of spinning or not, hence the different scenarios. Come what may the cylinder is spun before the first shot is fired. Then when a second salad is added you can opt to spin the cylinder either once or twice inbetween the two shots that are now to be fired.
so in the first part when the first salad is fired the cylinder is spun before the shot is taken, which is the same in all scenarios.
If no salad is fired, then a second is added and two further shots are fired, but you have the choice if you spin the cylinder before or inbetween each of the two extra shots.

krishnan
May 04, 2004
 Sorry, I did not read the question properly about the cannon being fired twice after putting salad in two chambers. That caused most of the confusion. The other thing that is confusing is the statement, 'spinning the cylinder after putting in the salad'. I did not know how this affected anything because the cylinder is spun anyway before the first shot. But now I realise it means spinning the cylinder after putting in the FIRST salad. Also, I think, in scenario 2, it should say, 'Since the cylinder is NOT spun after first shot' 
jimbo
May 04, 2004
 Scenario 4 says "Not spinning the cylinder either after putting in the salad or after taking the first shot". This contradicts what MadAde just said that the cylinder is always spun after putting in the salad. Between the first salad loading and the first firing, the cylinder is either spun or it isn't. You can't have it both ways.
Also, once the cylinder is spun, there must be a probability involved of 5/6 of being salad free befor the canon is fired again. It can't be 4/6 until the second loading. 
jimbo
May 04, 2004
 I think that what is intended is the following.
1. Spun fired P = 5/6 salad free.
Second load spun fired p = 4/6
Salad Free = 5/6*4/6 = 5/9 = 56% but this is not one of the answers.
2. Spun fired p = 5/6
Second load not spun but fired straight away. We do not know teh mechanics of the loading and firing process to know what chambers are now available for shooting if the cylinder is not spun???

jimbo
May 04, 2004
 Just to take the first clue given in the body. The probability of remaining salad free after the first shot is the same in each scenario. Well it must be 5/6 and not 4/6 surely? 
jimbo
May 04, 2004
 After reading MadAde's comment it appears that he is saying the canon is actually fired three times in all. I don't think this is clear in the original teaser. Perhaps the references to the "first shot" are actually to the first of the second two shots i.e. the second shot! 
madade
May 04, 2004
 We're interested in the probability of surviving 2 successive chances of copping a salad. If P1 is the probability we remain salad free the 1st trigger pull and P2 the probability we remain salad free the 2nd trigger pull, the probability we remain salad free both is P1*P2.
Regardless of how we insert 2 salads, there will always be 2 cylinders with salads and 4 without. So P1=4/6.
so if we veiw each case in turn.
1spin/spin
The 2nd spin gives us no information regarding the location of either salad. So P2=4/6 and the probability of surviving is 4/6 * 4/6=4/9=44.44%.
2spin/don't spin
Now either the 2nd salad is adjacent to the first (2 cases), or it is not (3 cases).
Letter the cylinders A B C D E F and have the adjacent salads in cylinders B and C.
Then we remain salad free the 2nd firing if our initial firing was D E or F, and get the salad if it was A.
If the salads are not adjacent, say A and C, we remain salad free the 2nd firing if our initial firing was D or E, and get the salad if it was B or F.
Total chances of remaining salad free are 4/6 * 2/5 * 3/4 + 4/6 * 3/5 * 1/2= 2/5 = 40%.
3don't spin/spin
Now the 2 salads are always adjacent, say in B and C, but the spin destroys that information. The probability of no salad is 4/6*4/6 = 1/2 = 44.44%.
4don't spin/don't spin
The 2 salads are adjacent again, say in positions B and C, but since we don't spin we remain salad free if our 1st pick was D E or F, die if it was A. The probability is 4/6*3/4 = 1/2 = 50%.
If this doesn't help please PM me and I will try to explain it more. 
Eigenvector
May 04, 2004
 This problem is worthless. Any good math problem should only be a few sentences long. It should be clear, concise, and direct. The author tries to make it "entertaining" by including a salad shooting canon. Unfortunately, making it silly also makes it way too wordy which is a nono in math questions. 
madade
May 04, 2004
 it is a good job that it is a probability teaser then, or I would look really daft.

jimbo
May 05, 2004
 But it says that only 1 round of salad is loaded at first, herefore the probability of being salad free after the first round is 5/6 not 4/6. It than says "If there is no loser, there is a second round where another load of salad is added, so now two chambers contain salad ". Only after the first shot is a second load of salad loaded so now, the second time the propbability of salad is 4/6.
I do not agree with eigenvector that Math or probability teasers must not be situated in interesting scenarios. But too often, probability problems depend on the semantics of teh problem as is the case here.
If the second salad is loaded but the cjamber is not spun, then the only possibilty is that the NEXT chamber to the last one fired will be fired this time. I am assuming that the empty chamber which has just been attempted to be fired is teh one in the firing position and so cannot be considered as available for the next round unless it is spun. But this is an assumption because I am not told anything about the loading process and how it relates to the firing sequience. If the chamber is spun, it is OK because all chambers are randomly available.
I'm getting the feeling that the problem is meant to state something like this:
2 lots of salad are loaded. The canon is fired once (4/6). One scenario is that the chamber is spun before firing again (4/6)[Answer 44%] while the other scenario is simply firing a second time(3/5) [Answer 40%]. However, with this interpretation I cannot see 4 different scenarios. 
(user deleted)
May 05, 2004
 I,too,agree with Jimbo. 
madade
May 05, 2004
 Damn, Thats the last time I try a probability teaser 
Palsha
May 05, 2004
 Don't you just love it when people pick apart every last detail of your teaser? It's happened to me and my advise to those who tend to look for flaws...."Don't give up your day job" 
madade
May 06, 2004
 I don't mind the comments, one way or another, but Jimbo is right. the wording needs altering. I will do it at some point....soon 
Palsha
May 06, 2004
 How did this one get passed the editors? Oh wait, nevermind...hehehe. 
madade
May 06, 2004
 can I just point out that editors are not allowed to edit their own teasers....so if it is wrong it is everyones elses fault.... 
Palsha
May 06, 2004
 Sorry mad, but you can't point that out my friend....hehehe. I know, just teasing with you! 
Eigenvector
May 10, 2004
 I would like to clarify my earlier comment. I think it's great when problems are made more interesting. That's part of the problem with mathematics for many, it's too dry. However, as Jimbo pointed out, getting too wordy is dangerous, especially with probability problems. A word here or there can completely change the problem. 
cnmne
Jan 11, 2005
 I have to agree with Jimbo and others about the wording of the teaser. It seems to be rather confusing as to when the chambers are spun. If this is due to my own density, I apologize. But there is one definite error. In the answer, there is a problem with scenarios 2 and 3. If you look at the second line of each scenario, the statements are the same, but the probabilities are different. I personally have no problem with creating a storyline in order to make the teaser more interesting. 
angelgirl1994
Mar 11, 2005
 That was a toughie. 
skimela
May 11, 2005
 missed the point of the question...but i like the scenario!! kebabs  yummy!! 
javaguru
Dec 09, 2008
 This "puzzle" is a poorlyworded mess of contradictions and the answer is wrong...why is it still here? 
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