Question

A 30-question test is such that 40% of the questions are hard (there is a 90% chance you will get them correct), 40% of the questions are very hard (there is a 50% chance you will get them correct), and 20% of the questions are ridiculously hard (there is a 10% chance you will get them correct. Correct answers are worth 5 points, wrong answers are worth -1 points, and you answer all the questions. What is the expected value of your score? (Oh, the irony...)

Answer 1

multiply the points you get by the probability you get them and add

Answer 2

(0.9)(5)(0.4)(30) + (0.5)(5)(0.4)(30) + (0.1)(5)(0.2)(30) - (0.1)(1)(0.4)(30) - (0.5)(5)(0.4)(30) - (0.9)(5)(0.2)(30)
Do I just do that?

Answer 3

yes

Answer 4

i would factor out the 30 but it makes no difference

Answer 5

i was about to write
\[30(5\times .9\times .4 -1\times .1\times .4+...\] but i think you have it exactly

Answer 6

Alright thanks!