Posted by kadane on January 29, 1998 at 18:50:37:
In Reply to: Probabilitly posted by Me on January 27, 1998 at 09:38:50:
: Say rather than flipping the same coin twice, you were to flip
: two different coins. How would that change the odds? I realize
: that it wouldn't change the probablity with a fair coin, but how
: about the other?
In the case in which a coin is drawn from a bag containing 1/6
double-headed coins, 1/6 double-tailed, and 2/3 fair coins, the
probability of a head on the first flip is 1/2, but if the same
coin is flipped twice, the outcomes of the two flips are dependent.
However, if a new coin is drawn for the second flip, then the flips
are independent, and the probabilities are the same as for a fair
coin.
An excellent question !
Professor Kadane