# Expected value of winning with a Random Uniform Variable

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.

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"What is the expected value of the money you'll earn?" Assuming you follow which strategy? –  Did Apr 27 at 9:22
No strategy needed. The probability that you answer correctly is somewhere between 0.3 and 1.0 –  ColacX Apr 28 at 6:41
Sure but at any time you have to decide whether to quit or to continue. –  Did Apr 28 at 7:02
I suppose the strategy then is to quit right after when you've won the expected value of money. But the strategy is not really the main concern. Oh when i mean the correct answer is 1.357 i meant if there is only 1 single question. –  ColacX Apr 28 at 8:19
Then the expected value of the money one will earn is 1.3, not 1.357. Sorry but your question is unclear. –  Did Apr 28 at 8:29