Theoretical and Experimental Probability

Date: 05/07/2001 at 15:51:50
From: Laura
Subject: Probability

Hi. My question is:

Michael is learning about probability. He spins a spinner 20 times 
and records the results. What might he conclude from his experiment?

The spinner is divided into 4 sections: 2 blue,1 yellow, and 1 red.

  a) The theoretical probability of spinning red is one-half.
  b) The experimental probability of spinning blue is three-fifths.
  c) The experimental probability of spinning yellow is 100.001%
  d) The theoretical probability of spinning red if four-fifths.

Supposedly the correct answer is B, but how?

Date: 05/08/2001 at 14:17:04
From: Doctor Twe
Subject: Re: probability

Hi Laura - thanks for writing to Dr. Math.

We can't determine anything about "theoretical" probabilities by 
experimentation - that has to be done by analysis of the situation (in 
this case, geometric analysis of the spinner and relative sizes of the 
blue, yellow, and red sections). So choices (a) and (d) can be 
eliminated.

One of the basic axioms of probability says that any probability has 
to be between 0 and 1 (0% and 100%) inclusive; it can never be less 
than 0 (0%) nor more than 1 (100%). So that eliminates choice (c).

The only one left is (b). Presumably, in order to get that 
experimental probability Michael must have landed on blue 
(3/5)*20 = 12 times.

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/