Game Description: Bob gives the contestant a free chip just for playing the game. The contestant climbs to the top of the Plinko board (see picture below) and drops the chips one at a time. The pegs send the chip bouncing all over the board until they land in slots representing money amounts at the bottom. The slots are, from left to right; $100, $500, $1000, $0, $10000, $0, $1000, $500, $100.

(a) For each of the three middle slots at the top of the board (slots 4, 5, and 6), find the probability that a chip starting in each slot results in winning $10,000.

(b) Compute the expected winnings for a chip dropped in slot 5 and the expected winnings for a chip dropped in slot 4 or 6.

slot Blot Blot shot slot Blot Blot 1 slot slot 2 3 4 5 7 8 9 $100 $500 $1000 $0 $10000 $0 $1000 $500 $100