perplexus.info :: Probability : Quiz Quandary

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?

Submitted by DJ

Rating: 3.7778 (9 votes)

Solution: (Hide)

set up a matrix for the probabilities.
Different probability outcomes depend on how one did on previous quizzes:
Well So-so Poor Well .80 .15 .5 So-So .2 .6 .2 Poorly .3 .15 .82
Using the matrix, multiplying itself 4 times will give us a matrix that will help show what the probability of doing well on the fifth quiz.
This matrix emulates the solution tree that one could make by hand.
The probability of doing well on the fifth quiz is .52184 or 52.184%.
The probability of doing well on the fifth quiz if one did well on the first quiz is 52.2%.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-04-12 21:15:44
re: i think...	EvelynA	2020-08-17 23:33:45
Solution	Math Man	2018-08-26 13:16:45
re(2): Markov chains	Finkle	2003-12-27 19:21:26
re: Markov chains	Charlie	2003-12-27 09:32:25
Markov chains	Federico Kereki	2003-12-27 01:12:39
re(2): Solution (only a common calculator used)	Penny	2003-12-26 22:56:32
re: Solution (only a common calculator used)	Charlie	2003-12-26 22:36:38
re: Solution (only a common calculator used)	Bruno	2003-12-26 22:35:40
Solution (only a common calculator used)	Penny	2003-12-26 20:58:34
re: Depends...	Charlie	2003-12-26 15:02:42
Depends...	Charlie	2003-12-26 14:49:56
Well well well	Bruno	2003-12-26 14:19:04
i think...	sarah	2003-12-26 14:18:09

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