Got many correct answers for this puzzle, particularly pleased that Mahi, Suman’s daughter also answered this correctly. Other people to send correct answers included Suman Saraf, Bhanu, Pratik Poddar and Karan Sharma, my nephew. Well done all.
The boy maximizes his chance of drawing a $10 bill by putting a single $10 bill in one hat, and the other 19 bills (9 $10 bills and 10 $1 bills) in the other hat. If one set is one 10 dollar bill and the second set is the rest of the nineteen bills (ten 1s and nine 10s) then the probability of picking a 10 dollar bill is 1/2*(1+9/19) or 14/19 or .737.
Hope you all enjoyed the puzzle.