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Calculus killed any interest I had in mathematics long ago. Disliked and Unsubscribed.
Suppose you have a deck of 4 cards: Son of God, New Jerusalem, Christian Martyr and Burial.You draw 2 of the cards, but don't look at them.I look at the two remaining cards. Suppose I told you that one of the cards you drew was a good dominant. Knowing that, what are the odds you drew both good dominants?Now suppose I told you that you for sure drew Son of God. Knowing that, what are the odds you drew both Son of God and New Jerusalem? Are the odds the same or different?
The first thing I'd have to do is figure out the probability that you are lying If I decided to assume that you weren't lying, I could get on with the problem.There are 24 ways the deck can be arranged, in 4 of them do you draw both Good Dominants. Of the 24 options 4 are removed if you know you drew at least 1 good dominant, leaving you with 4 options out of 20, or 1/5. From there an additional 8 options are removed if you know one of the dominants is Son of God, leaving you with 4 options out of 12, or 1/3.
There are 24 ways the deck can be arranged...
Quote from: ChristianSoldier on December 12, 2016, 03:33:16 AMThere are 24 ways the deck can be arranged...You can save yourself some time if--instead of starting with the full deck--you only worry about the two drawn cards (12 ways to draw the two cards). This can also be simplified by realizing that the order of the draw is *not* important in this case. So there are actually only six combinations to worry about: SN, SC, SB, NC, NB, and CB.
QuoteThe first thing I'd have to do is figure out the probability that you are lying If I decided to assume that you weren't lying, I could get on with the problem.There are 24 ways the deck can be arranged, in 4 of them do you draw both Good Dominants. Of the 24 options 4 are removed if you know you drew at least 1 good dominant, leaving you with 4 options out of 20, or 1/5. From there an additional 8 options are removed if you know one of the dominants is Son of God, leaving you with 4 options out of 12, or 1/3.Winner!!!
It seems intuitively that the answer should be 1 in 3 for both. If I tell you one card is SoG, the odds are 1 in 3 you also drew NJ. Likewise, if I told you one card is NJ, the odds are 1 in 3 you also drew SoG. It's therefore reasonable to think that if I tell you one card is a good dominant, that the odds would remain 1 in 3 that you drew the other one. However, because we don't know which good dominant was drawn, there a couple more "losing" combinations that are possible (which are not possible when we know exactly which good dominant we drew).Here are the 12 two card combinations you can draw: (S=SoG N=NJ C=CM B=Burial)S-NS-CS-BN-SN-CN-BC-SC-NC-BB-SB-NB-CIf we know we drew SoG, we can see there are 6 possible combos that involve SoG. Two of those combos also include NJ so when you know one of the cards is SoG, there is a 2 in 6 (1 in 3) chance that you also hold NJ.If we only knew we drew a good dominant (but not which one), we see there are 10 combinations that involve either SoG or NJ. Two of those include both SoG and NJ therefore we have 2 "winning" combinations out of a possible 10 which gives us odds of 2 in 10 (1 in 5).
Quote from: Master Q on December 11, 2016, 07:49:01 PMCalculus killed any interest I had in mathematics long ago. Disliked and Unsubscribed. And yet your inner calling for mathematics Jesus brought you into this thread. Suppressing that innate love for math Jesus will only leave you unfulfilled and incomplete.
For the odds of drawing both good dominants, there is a 1 in 2 chance that you drew a good dominant the first time since there are 2 good dominants, and 2 evil dominants. The odds of drawing a good dominant the first time is 2 out of 4 which is also 1 in 2, then the odds of pulling the 2nd good dominant assuming that you have successfully already drawn the first good dominant there is a 1 in 3 chance.So all in all, the chance of pulling both good dominants is 1 in 6.