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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: Solution (only a common calculator used) | Comment 7 of 12 |
(In reply to Solution (only a common calculator used) by Penny)

The transition probability from B to G is 0.03--not 0.3. (1 - 0.15 - 0.82 = 0.03).

Given the use of the wrong probability, there are also some arithmentic mistakes:
(0.8)(0.15)(0.6)(0.2) = 0.0144, not 0.0010368.
(0.15)(0.2)(0.05)(0.3) = 0.00045, not 0.0003
(0.05)(0.82)(0.82)(0.3) = 0.010086, not 0.00413526

The array should (using the correct 0.03) look like

```
GGGG           .8  .8  .8  .8             0.409600

GGMG           .8  .8  .15  .2            0.019200

GGBG           .8  .8  .05  .03           0.000960

GMGG           .8  .15  .2  .8            0.019200

GMMG           .8  .15  .6  .2            0.014400

GMBG           .8  .15  .2  .03           0.000720

GBGG           .8  .05  .03  .8           0.000960

GBMG           .8  .05  .15  .2           0.001200

GBBG           .8  .05  .82  .03          0.000984

MGGG           .15  .2  .8  .8            0.019200

MGMG           .15  .2  .15  .2           0.000900

MGBG           .15  .2  .05  .03          0.000045

MMGG           .15  .6  .2  .8            0.014400

MMMG           .15  .6  .6  .2            0.010800

MMBG           .15  .6  .2  .03           0.000540

MBGG           .15  .2  .03  .8           0.000720

MBMG           .15  .2  .15  .2           0.000900

MBBG           .15  .2  .82  .03          0.000738

BGGG           .05  .03  .8  .8           0.000960

BGMG           .05  .03  .15  .2          0.000045

BGBG           .05  .03  .05  .03         0.000002

BMGG           .05  .15  .2  .8           0.001200

BMMG           .05  .15  .6  .2           0.000900

BMBG           .05  .15  .2  .03          0.000045

BBGG           .05  .82  .03  .8          0.000984

BBMG           .05  .82  .15  .2          0.001230

BBBG           .05  .82  .82  .03         0.001009

```

------
Totalling .52184185.

Maybe your calculator needs a repair for its intermittent problems.
 Posted by Charlie on 2003-12-26 22:36:38

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