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 Quiz Quandary (Posted on 2003-12-26)
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: 4.2857 (7 votes)

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 re: Depends... | Comment 4 of 12 |
(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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