Create quant.md

problem-of-the-day/day19/quant.md

@@ -0,0 +1,13 @@
+A dealer at a casino holds a game that is played as
+follows: The player first pays $d to the dealer, where d
+is some positive integer less than 100. The dealer then
+intends to flip a coin d times. If at any point two
+consecutive heads are flipped, then the dealer stops
+flipping the coin, and the player wins and is awarded
+$100. Otherwise, the player loses (and is awarded
+nothing). A player pays the dealer $29. The dealer
+weights the coin before flipping it, changing the
+probability of flipping heads such that the player's
+expected net profit is non-positive. The player is not
+aware of this re-weighing. Find the maximum
+probability that the dealer should choose.