A new lie detective test has been devised and must be studied before it is put into use. Three hundred people are selected at random, and each person draws and keeps a card from a box of 300 cards. Half the cards instruct the person to lie and the others instruct the person to tell the truth. Of those who lied, 90% fail the new lie detector test (failing the test indicated lying). Of those who told the truth, 4% failed the test.

Give answers as decimal numbers.

1. (A) What is the probability that a randomly chosen subject who lied passed the test?

(B) What is the probability that a randomly chosen subject told the truth and failed the test?

(C) What is the probability that a randomly chosen subject failed the test?

(D) What is the probability that a randomly chosen subject will have lied given that the subject failed the test.

(E) According to this study, if 50 new subjects are told to lie when they take the test, what probability that exactly 45 of them fail the test?

2. Solve the equation. Type the answer in ascending order (smallest to largest) with a comma between and no spaces. Your answers should be exact numbers (fractions and not decimal approximations).

x=152x^2