- Alka is considering paying \(\pounds 5\) to play a game. The game involves rolling two fair six-sided dice. If the sum of the numbers on the two dice is at least 8 , she receives \(\pounds 10\), otherwise she loses and receives nothing.
If Alka loses, she can pay a further \(\pounds 5\) to roll the dice again. If both dice show the same number then she receives \(\pounds 35\), otherwise she loses and receives nothing.
- Draw a decision tree to model Alka’s possible decisions and the possible outcomes.
- Determine Alka’s optimal EMV and state the optimal strategy indicated by the decision tree.