Originally Posted by BabyRain #59 (15 points) Taxloss, Brain and xmichelly are doing a shooting duel, they are in a forest and each of them has a gun. These are the rules: -They first need to play (bao-chieng-tap) rock-paper-scissors to decide who may shoot first, second and third. -In that order they need to fire at each other until there is one survivor. -They may decide on who they are oging to shoot -We know that Taxloss NEVER misses, Brain only misses 20%, xmichelly is still so unexperienced that she misses 50% of all the times -They all have a strategie -They won't die because the original target dodges and it hit the other target. (e.g. if Brain shoots at Taxloss and it misses, it won't hit xmichelly.) Who has the greatest chance to survive this and how big is that chance? ---------------------------------------- XMichelly will have the biggest chance of survival bcoz taxloss and brain will want to shoot at each other to take out the biggest threat. Assuming Taxloss shoots first, taxloss will want to shoot at Brain... brain dies... xmichelly's turn to shoot.. Assuming Brain shoots first, Brain shoots at taxloss, if succeeds, taxloss dies n xmichelly's turn to shoot at brain. If brain misses, taxloss shoots, oso wanna shoot at brain first... so brain dies, xmichelly shoots at brain. If Xmichelly shoots first, she should shoot somewhere else... then it's either taxloss or brain's turn to shoot.. and eventually Xmichelly's turn. Well if u are talkin about the best chance of survival out of the three, Xmichelly has 66% chance to survive?
#58 (15 points) Hiake, BRain, Taxloss, Xiaojia and xmichelly robbed a bank and have stolen 1000 pieces of gold. Hiake is the boss of this group and xmichelly is ranked the lowest. However, they want to share these gold. Starting from the lowest rank (michelly) each of them are allowed to make a suggestion of how to divide these golds. If the majority of the group votes against it, the person that has suggested will be killed. If the majority accept it, then it will be divided as suggested. Each of them are: VERY smart, they have a BIG lust for money, they DONT CARE if any of their group dies, they do want to LIVE though. So what will xmichelly suggest without getting killed? =============== Dunno if this got to do with maths.. so wild guess first Since there are 5 of them, xmichelly can say "I suggest the 3 of us, (name another 2 names) get the biggest share... so the majority of the vote = 3 people (includin herself) won't vote to kill her ...
#54 (19 points) Guess the number X 0<X<564 Everytime someone has made a guess, ill adjust it. So for example if Taxloss says 600, and X is lower than 600, it will be adjusted to 0<X<600. When this happens, there will be 1 point substracted from the reward. So now it only will worth 19 points. This go on till it reaches 0 and this assignment will be gone. You are not allowed to answer multiple time behind each other, you need to wait for another person to guess first. The person that has guessed the correct number gets the points. X = 300
almost, still wrong the other two want more, so they will probably say no too. They have a very big lust for money 0<X<300
xmichelly suggests to kill the mean boss Hiake so they can divide the share without having to kill each other?
here ya go...#32... its err very badddd....took one shot at it...and err cba to re do it... so i err some bits are slurred.... eh whatever....
Shit i should get more points for this lol. It's more troublesome than writing story. #59 (15 points) Taxloss, Brain and xmichelly are doing a shooting duel, they are in a forest and each of them has a gun. These are the rules: -They first need to play (bao-chieng-tap) rock-paper-scissors to decide who may shoot first, second and third. -In that order they need to fire at each other until there is one survivor. -They may decide on who they are oging to shoot -We know that Taxloss NEVER misses, Brain only misses 20%, xmichelly is still so unexperienced that she misses 50% of all the times -They all have a strategie -They won't die because the original target dodges and it hit the other target. (e.g. if Brain shoots at Taxloss and it misses, it won't hit xmichelly.) Who has the greatest chance to survive this and how big is that chance? ---------------------------------------- XMichelly will have the biggest chance of survival bcoz taxloss and brain will want to shoot at each other to take out the biggest threat. Assuming Taxloss shoots first, taxloss will want to shoot at Brain... brain dies... xmichelly's turn to shoot.. Assuming Brain shoots first, Brain shoots at taxloss, if succeeds, taxloss dies n xmichelly's turn to shoot at brain. If brain misses, taxloss shoots, oso wanna shoot at brain first... so brain dies, xmichelly shoots at brain. If Xmichelly shoots first, she should shoot somewhere else... then it's either taxloss or brain's turn to shoot.. and eventually Xmichelly's turn. p = probability P(Tax hits) = 1 P(Tax misses) = 0 P(Brain hits) = 4/5 P(Brain misses) = 1/5 P(xMichelly hits) = 1/2 P(xMichelly misses) = 1/2 ===== Shooting order Tax, Brain, Xm So T shoots B, which means that P(T,TBX) = 1/2, P(B,TBX) = 0, and P(X,TBX) = P(X,XT) = 1/2 Tax, Xm, Brain So T shoots B, which means that P(T,TXB) = 1/2, P(B,TXB) = 0, and P(X,TXB) = P(X,XT) = 1/2 Brain, Tax, Xm Brain must shoot T for a chance of survival, else Brain = 0 chance of survival, since tax will surely shoot at Brain and sure kill. P(B hits) × P(B,XB) + P(B misses) × P(B,TXB) = 16/45 So B shoots T, which means that P(B,BTX) = 16/45, P(T,BTX) = P(B misses) × P(T,TXB) = 1/10, and P(X,BTX) = P(B hits) × P(X,XB) + P(B misses) × P(X,TXB) = 49/90 Brain, Xm, Tax Brain must shoot at tax: So B shoots T, which means that P(B,BXT) = 16/45, P(T,BXT) = P(B misses) × P(T,XTB) = 1/10, and P(X,BXT) = P(B hits) × P(X,XB) + P(B misses) × P(X,XTB) = 49/90 Xm, Tax, Brain X should deliberately not shoot either one, since the surviving chance is the highest P(X,TBX) = 1/2 So X should miss deliberately, which means that P(X,XTB) = 1/2, P(T,XTB) = P(T,TBX) = 1/2, and P(B,XTB) = P(B,TBX) = 0 Xm, Brain, Tax X deliberately miss again. Xm surviving chance will be P(X,BTX) = 49/90 P(X,XBT) = 49/90, P(T,XBT) = P(T,BTX) = 1/10, and P(B,XBT) = P(B,BTX) = 16/45 Shooting order: Survival chance of C: TBX P(X,TBX) = 1/2 TXB P(X,TXB) = 1/2 XTB P(X,XTB) = 1/2 XBT P(X,XBT) = 49/90 BTX P(X,BTX) = 49/90 BXT P(X,BXT) = 49/90 Total : 47/90 52.22%
#58 (15 points) Hiake, BRain, Taxloss, Xiaojia and xmichelly robbed a bank and have stolen 1000 pieces of gold. Hiake is the boss of this group and xmichelly is ranked the lowest. However, they want to share these gold. Starting from the lowest rank (michelly) each of them are allowed to make a suggestion of how to divide these golds. If the majority of the group votes against it, the person that has suggested will be killed. If the majority accept it, then it will be divided as suggested. Each of them are: VERY smart, they have a BIG lust for money, they DONT CARE if any of their group dies, they do want to LIVE though. So what will xmichelly suggest without getting killed? ============= if they kill off xmichelly, XJ, tax, left brain n hiake.. hiake would say no to whatever brain says, n kills her.. Get everything. So... To survive, brain shd say yes to whatever tax is suggesting. So tax cld say take all the 1000 for himself, n brain wld still agree, knowin hiake wld definitely kill her. Now in order for xj to survive, xj must get 3 approval out of 4 people... so she could say give 1 coin to Brain n hiake... since tax is suggestin 1000, so hiake n brain know they wun get anything at all if they dun agree to xj. For xmichelly to survive, she needs 3 approval out of 5 too, since in xj's turn, tax won't get anything, xmichelly needs to offer tax 1 coin for her to agree. then xmichelly needs to offer either hiake or brain 1 coin for them to agree as well. no point to offer xj because xj wants 998 coins to herself when it comes to her turn.
