At a charity event there is a money-raising game involving a pair of ordinary dice. The game costs $a to play. When the two dice are rolled, their sum is described by the variable X. The organisers decide that a sum which is less than 4 or between 7 and 9 inclusive is a loss of $ a 3 , a result between 4 and 6 inclusive gives a return of $7, and a result of 10 or more gives a return of $21. a Determine P(X 6 3), P(4 6 X 6 6), P(7 6 X 6 9), and P(X > 10). b Show that the expected gain of a player is given by 1 6 (35 7a) dollars. c What value would a need to have for the game to be fair? d Explain why the organisers would not let a be 4. e If the organisers let a be 6 and the game was played 2406 times, estimate the amount of money raised by this game.

Kasebier: woman in photography Showed at Alfred Stieglitz’s photo gallery Common subject: mother + child, involving allegory and suggested that being a good wife and mother is a moral important thing Art for art’s sake Soft and painterly Gum print: type of print you can manipulate in the negative and in the print to make it painterly Signed the work to signify that they are artists ▯ 1913: Armory Show in NY, showed European + American modernists First major show that helped bring modernism to America Cubism was not taken well by the public “shingle explosion” Stieglitz had already been showing modernism in his gallery but this show is what made it mainstream to pu