Probability

[Hira Javaid]

I have done it's first part. For part b will we be finding P(last question is easy for easy exam)+ P(P(last question is easy for hard exam). Don't have idea about part c

A professor gives only two types of exams and designs only two types of questions, “easy” and “hard”.
You will get a hard exam with probability 0.80. The probability that the last question on the exam is hard
is 0.90 if the exam is hard; the probability that the last question on the exam is hard is 0.15 if the exam is easy.
a) What is the probability that you will get an easy exam?
(b) Before you attend an exam, estimate what is the probability that the last question on your exam will
be easy.
(c) Now you have attended the exam. The last question on the exam turned out to be hard. What is the
probability that you have attended an easy exam?

 

[Dr.Peterson]

I have done it's first part. For part b will we be finding P(last question is easy for easy exam)+ P(last question is easy for hard exam). Don't have idea about part c

A professor gives only two types of exams and designs only two types of questions, “easy” and “hard”.
You will get a hard exam with probability 0.80. The probability that the last question on the exam is hard
is 0.90 if the exam is hard; the probability that the last question on the exam is hard is 0.15 if the exam is easy.
a) What is the probability that you will get an easy exam?
(b) Before you attend an exam, estimate what is the probability that the last question on your exam will
be easy.
(c) Now you have attended the exam. The last question on the exam turned out to be hard. What is the
probability that you have attended an easy exam?

This is where you can use Bayes Theorem. Have you tried it?

Alternatively, I just make a 2x2 table (rows for the exam being hard or easy, columns for the last question being hard or easy), and fill it out with the data, and the question is easy to answer from that.

Your description of (b) is not right as stated, but you likely mean the right thing. Your word "for" sounds like it could mean "given", but if you change it to "and" you will be right.

 

[Hira Javaid]

I tried bayes theorem but i am not getting it exactly. But if i do the row thing...should i take the determinant of it or just multiply and add them

 

[Dr.Peterson]

I tried bayes theorem but i am not getting it exactly. But if i do the row thing...should i take the determinant of it or just multiply and add them

Please show your work, so we can see in what way you "tried Bayes' theorem", and what went wrong.

"The row thing" has nothing to do with matrices and determinants; I have no idea what you are thinking of. I was referring to the kind of table they use here: https://www.mathsisfun.com/data/bayes-theorem.html