A college student estimates the probability of passing a cou

A college student estimates the probability of passing a course. She
calculates that there is a 90 percent chance that she will pass the course if she attends all of the
classes, a 40 percent chance if she attends half of the classes, and a 10 percent chance that if
she does not attend any of the classes. The probabilities that she will attend all, half and none
of the classes are 0.7, 0.2 and 0.1, respectively.
a) What is the probability that she will pass the course?
b) Given that she passed the course, what is the probability that she will attend all of the
classes?
c) Given that she failed course, what is the probability that she will attend none of the
classes?

Solution