Question

Suppose a large group of a million people take the 4-question quiz, guessing their way through it just as you have. The possible "scores" on this quiz would be 0 (missing all four questions), 1, 2, 3, or 4 (getting all four questions "right").

What do you think the average score would be? Explain.

Answer 1

the quiz has n = 4 questions, each question has two possibilities either it is correct or incorrect each with probability p = 0.5 (50-50 chance to each)

Let X: number of correct answer (score) an individual gets. The exact distribuuton of X would be Binomial(n = 4, p = 0.5)

The expected value of X is given by

E(x) = n*p = 4*0.5 = 2

Even 1,000,000 group of people takes the quiz, for each of the person the expected score is 2 and average of 1,000,000 people would again be 2

Hence, average score would be 2