Expected numbers of 'yes' for following data
A = [1,2,3,5] B = [5,6,7,8]
A 'yes' is when a^b > b^a where a is value randomly chosen from A and b is value randomly chosen from B . Also numbers a and b are discarded from A and B after randomly chosen.
Please explain how to solve it.
Hint: There are only $16$ possibilities, so you can go through them. All with $1$ from $A$ will be no, all with $2$ or $3$ will be yes, and $5$ will be yes unless it is paired with $5$. Presumably you are picking four disjoint pairs and looking for the count of the pairs which produce yes.