I have this small homework I don't quite understand.
The problem is formulated as a game. (Who wants to be millionaire)
You start with 1£. money = 1.0£
You can choose to quit at anytime So you can quit immediately without answering and still have 1£.
You will be given a question with a probability p of answering correctly.
If you answer wisely you double up and get 2£. If you answer poorly you lose everything and get 0£.
The probability p is not exactly known but is a uniform distributed variable between 0.3 and 1.0
What is the expected value of the money you'll earn? E(money). The correct answer is 1.357 if there is only one question.
My best guess is p = (1.0 + 0.3)/2
E(money) = 1.0 + 2.0*p - 1.0*(1-p) = 1.95 which is the wrong answer...
My homework is about finding an algorithm for more than 1 question, however i fail to understand for just 1.
Thanks for any help.