An examination consists of multiple choice questions, each having five possible answers. Linda estimates that she has probability 0.75 of knowing the answer to any question that may be asked. If she does not know the answer, she will guess, with the conditional probability 1/5 of being correct. What is the probability that Linda gives the correct answer to teh question.

How would you go about solving this question. I know the answer is 0.8 - says so in the back of my book. However, I'm curious to how this was derived.

A tree diagram makes it clear:

The first two branches are knowing (Pr(knowing) = 0.75) or not knowing (Pr(not knowing) = 0.25). Then the next two branches are guessing (correct or not correct).

I get (0.75) + (0.25)(1/5) = 0.75 + 0.05 = 0.8.

__________________
There are two things you should never try to prove: the impossible and the obvious.

The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)

• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.