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 soso, and a 5% chance you will do poorly.
If you did soso on a quiz, there is a 20% chance you will do well on the next quiz, a 60% chance you will do soso, 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 soso, 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?
(In reply to
Solution (only a common calculator used) by Penny)
The transition probability from B to G is 0.03not 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 20031226 22:36:38 