Let X be the random variable number of correct questions.
X ~ Binomial(n = 8, p = 1/4).
Calculate Pr(X = 8), Pr(X = 7), Pr(X = 6) and Pr(X < 6).
Now calculate the expected profit. What does this tell you about the minimum number of questions you need to know the answer to so that the expected profit is greater than zero?