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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)

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re: Depends... | Comment 4 of 11 |
(In reply to Depends... by Charlie)

By the way, in going through various scenarios in the independent-tests assumption, 7 of the desired statistics could be made to come out exactly, as in the following set of the three tables presented:


Well Soso Poorly
Bright 0.888224 0.072408 0.039369 0.360933
Avg 0.142968 0.727862 0.12917 0.301099
Low 0 0.081176 0.918824 0.337969

p(bright) 0.88162 0.095825 0.039076
p(avg) 0.11838 0.80358 0.106956
p(low) 0 0.100595 0.853968

had done well 0.8 0.15 0.049999
had done soso 0.2 0.6 0.2
had done poor 0.049999 0.15 0.8

-------
Excel consistently made the probability of doing poorly given having done well equal to the probability of doing well having done poorly, here 5%, in order to get exact matches on the others.

(this was with a simpler, 3-ability-level, scenario than was previously given.)
Edited on December 26, 2003, 3:03 pm
  Posted by Charlie on 2003-12-26 15:02:42
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