8 questions on true/false quiz. Expected number of correct answers with a given probability of correct answer of a question "i". The odds/probability of a correct answer of question $i$ is $p=1-2^{-i}$
What is the expected number of correct answers?
My attempt:
$$(1-2^{-1})\cdot
(1-2^{-2})\cdot
(1-2^{-3})\cdot
(1-2^{-4})\cdot
(1-2^{-5})\cdot
(1-2^{-6})\cdot
(1-2^{-7})\cdot
(1-2^{-8})\cdot= 0.28991911785$$
$$0.28991911785 \cdot 8 = 2.3193529428$$
$$= 2 \text{ questions correct}$$

Thanks for showing your work.
Your fisrt line computes the probability that all answers are correct. 
The expected number of correct answers is not just $8$ times this probability.
Think of it differently: The expected number $E_i$ of correct answers you get from question $i$ is simply $p_i=1-2^{-i}$ (more completely, it is $1\cdot p+0\cdot(1-p)$). The expected number of correct answers of the whole quiz is then $E=E_1+\ldots + E_8$.
