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Quiz Quandary (Posted on 2003-12-26) Difficulty: 3 of 5
A teacher said that she had observed that how well a student does on a particular quiz depends on how well or poorly he or she did on the last quiz. Then she gave the following statistics:

If you did well on a quiz, there is an 80% chance you will do well on the next quiz, a 15% chance you will do so-so, and a 5% chance you will do poorly.

If you did so-so on a quiz, there is a 20% chance you will do well on the next quiz, a 60% chance you will do so-so, and a 20% chance you will do poorly.

If you did poorly on a quiz, there is a 3% chance you will do well on the next quiz, a 15% chance you will do so-so, and an 82% chance you will do poorly. The teacher then asked the following question (which she said we'd be able to answer once we had successfully completed the class):

If you did well on the first quiz, what is the probability that you will do well on the fifth quiz in the class?

See The Solution Submitted by DJ    
Rating: 4.1667 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Markov chains | Comment 10 of 11 |
(In reply to Markov chains by Federico Kereki)

"first element of the vector [1 0 0]T times A^5."

Since you're going from the first to the fifth test, isn't it A^4? That is, multiplying by A^1 would get you to the second test, so A^4 would get you to the fifth.


  Posted by Charlie on 2003-12-27 09:32:25

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