You have a set of N elements. You choose, at random, a subset of it. Then, indep

Question

You have a set of N elements. You choose, at random, a subset of it. Then, independently, you choose another subset of the original set of N elements. There are no limits on the size of either of the subsets, each can contain anywhere from zero to N elements. Neither size is specified. What is the probability p that the second subset is a subset of the first? Eliminate (cross out) as many wrong answers as you can from the list below, and briefly explain why next to each. Remember that an empty (zero elements) set is a subset of any set, and a set is obviously a subset of itself. 1/N (3/4)^N (1 + 1/N)^N (1 + 1/N)^-N (1/2)^N p > 1/2

Explanation / Answer

given second subset is subset of first subset let x and y are two subsets of N

X + Y = N where X<= N , Y <= N ,

and Y <= X

P( Y / X ) = (N - X )/ N = 1 - (X/ N ) = (1 + 1 / N )-N = ( N / N+1 )N

option A and C are eliminted which are not possible and remaining options have chance to take place.

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