posted by PetarI .
Over time, a student analyzes her ability to guess correctly after narrowing down multiple choice answers in a 5-selection question (a through e). She discovers that if she narrows her answers to 2 or 3 choices, her probability of getting the right answer is 0.8, but if she still has 4 or 5 choices left, her probability of choosing correctly decreases drastically to 0.1. Assuming that in general she can narrow his choices to 2-3 choices 70% of the time, answer the following probability questions.
a. What is the probability that she will answer a question correctly any time she must guess?
b. Given that the student answered correctly, what is the probability that she had narrowed her choices to 2-3?