Question

2. I4] Prior to a test, 1/3 of a class of students study, and do so for n hours, where 0<ns 4 (n does not have to be an integer here). The other 2/3 of the class do not study at all. Those who study have a probability of ns of passing the test, and those who do not study have a 20% chance of passing. 117096 of all students that passed the test actually studied, what is a reasonable estimate for the length of thetir have of "4 of passing the test, and those wh n+1 study time? Hint: Use Bayes' Theorem to solve

Answer 1

P(pass the test)=P(study and pass)+P(not study and pass)

=(1/3)*(n+1)/5+(2/3)*0.2

hence P(studied|pass)=P(study and pass)/P(pass)=((1/3)*(n+1)/5)/((1/3)*(n+1)/5+(2/3)*0.2)=0.7

(n+1)/15 =0.7*(n+1)/15+0.28/3

0.3*(n+1)=1.4

n+1 =4.667

n=3.667~ 4