Fair price of a dice-product game

Roll two fair dice; the game pays you the product of the two faces in dollars - except if either die shows a 1, the game pays nothing. What is the fair price to play (the expected payout, in dollars, to four places)?

Show hints (2)+
  1. Independent dice: E[XY]=E[X]E[Y]=12.25E[XY]=E[X]E[Y]=12.25 before voiding.
  2. Sum surviving products over all 36 pairs: (2+3+4+5+6)2/36(2{+}3{+}4{+}5{+}6)^2/36 - divide by 36, not 25.

Answer

Reveal answer →

11.1111 (± 0.001)

Want the full step-by-step worked solution? It's part of Premium - along with a worked solution for every question in the bank.

Asked at: Timed Mental-Math & Sequences, Game-Based Aptitude

Related questions