It is a Binomial experiment as we are doing the same bernouli experiment repeatedly.
Which is the Bernouli experiment here ? Visiting a question and checking whether it is a correct answer or not. Why it is a Bernouli experiment ? Because a question can have either correct answer(success) or wrong answer(failure).
Total number of questions we are visiting,n = 1000*150 = 150000.
Let X be a random variable which indicates number of correct answer among the total of 150000 questions.
E(X) (i.e) Expectation of X (i.e) Expected number of correct answers = n * p (since it is a binomial experiment)
where n is no: of Bernouli experiments and p is probability of success (i.e) probability of correct answer.
Here n = 150000 , p = 0.25
Expected number of correct answers = 150000 * .25 = 37500.
Expected number of wrong answers = 150000 - 37500 = 112500.
Expected Total marks = Expected number of correct answers * number of marks per correct answer + Expected number of wrong answers * number of marks per wrong answer.
= [37500 * 1] + [112500 * (-.25)]
= 37500 - 28125