A coin is to be tossed until a head appears twice in a row.What is the sample space for this?

The sample space is the two possible outcomes of each trial: heads and tails. The question boils down to the probability that the second trial will be tails and the third and fourth heads, with the first trial being either. The probability of this is one-eighth (0.125 or 12.5%).

To solve the more general problem of finding a probability density function for the number of trials needed, I would start with a geometric distribution and see what happens. (Although I think we'd end up with a negative binomial distribution. )Good luck!

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.