Suppose a student who is about to take a multiple choice has only learned 83% of the material covered by the exam. Thus, there is an 83% chance that she will know the answer to a question. However, even if she doesn't know the answer to a question, she still has a 20% chance of getting the right answer by guessing. If we choose a question at random from the exam, what is the probability that she will get it right?

Question

anonymous · Answer

do you have a guess, or do you need all the work?

anonymous · Answer

I need the work as well...

anonymous · Answer

Just so I can understand it.

dape · Answer

Sometimes it's easier to understand probability if you throw in some numbers, so let's say that there is exactly 100 questions on one exam, and they cover all over the material equally. That means that the student would know the answer to 83 of the questions.

Now there is 17 questions left that the she can guess on, with 20% chance of being right. So on average she would be right on 17*0.2 = 3.4 questions more for a total of 83+3.4=86.4 questions.

Now let's say that we pick a question at random from this exam, then we would expect her to get it right 86.4 of 100 times, or 86.4% chance of getting it right.

Hope this helps.

anonymous · Answer

great explanation
the calculation would be $.83\times 1+.17\times .2$