Originally Posted by SkinnyGoomba
The last 5 pages have made me glad that I drink scotch and cognac.
Originally Posted by gomestar
yeah, the point was if one bottle is suspect and you're not sure if it's corked or not, go out and buy another because the odds of two bottles in a row being corked are exceedingly low.
Are you sure about this, mathematically? P(A and B) where A=bottle 1 corked and B=bottle 2 corked. In case we don't know about either bottle it's 1/200, if we assume that a bottle is corked with P=7/100. In your scenario however, we know that bottle 1 is corked, so the probability of bottle 1 being corked is 100%, therefore P(A and B) = 100/100*7/100=7/100. It's like throwing two dices. For (6,6) it's 1/36 (1/6*1/6), for any doubles however it's 1/6=[(1/6)*1/6)]*6. Same as seeing the "any doubles" as event A = throw 1 is fixed (or bottle one is corked) and event B = has to match number X with prob. 1/6 (or has to match "corked" with prob 7/100).
Other example is flipping a coin. The probability of heads is 1/2 (we assume that it never lands on the side). The probability of flipping three heads in a row is 1/2*1/2*1/2=1/8; for two in a row it's obviously 1/4. If you just flipped a head (have a corked bottle) and want to flip another head (open another corked bottle), the probability is 1/2 (7/100) and not 1/4 (5/200).
Lots of words for a small statement but I hope I make sense.