A die game is played by rolling a die and trying to guess the number rolled. You have two guesses to try and get the correct number. If your first guess is incorrect, before you make your second guess you will be told whether the correct number is higher or lower than your first guess.

(a) Using probabilities determine a strategy that will give you the best chance of winning. Give a detailed explanation of your findings.

(b) What is the probability of winning the game if you use the optimal strategy?

Why don't we choose we choose 2 or 5? For instance, I pick 2. if my first time is wrong, then I still have 25 % if the correct answer is greater than 2. If the correct answer is smaller than 2, I have 100% to guess it correctly. For part b), the probability= 1/6+(1/4)*1+1*(1/4)=2/3