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Bubbles in the Glass


Date: 05/22/99 at 03:43:32
From: Lawrence Bushell
Subject: Probability

Q. In a glass manufacturing process the probability of a glass having 
   bubbles is 0.03.

   The probabilty of it's being discoloured is 0.05.

   The probability of being both discoloured and having bubbles is 
   0.01.

   What does this say about the statements "The probability of it's 
   being discoloured is 0.05" and "the probability of a glass having 
   bubbles is 0.03"?

A. I got as far as concluding that if you get one defect the chance of 
   also getting the other is higher:

   If you have a bubble  0.03 * ? = 0.01, i.e. ? = 1/3

   If you have discolouration  0.05 * ? = 0.01, i.e. ? = 0.2.

But I got stuck there. Is there anything else to be worked out or 
concluded?


Date: 05/22/99 at 05:15:22
From: Doctor Anthony
Subject: Re: Probability

This means that the probability of having bubbles and the probability 
of being discoloured are not independent.

The test of independence for two events A and B is 

    P(A and B) = P(A).P(B)

If this equation is true then A and B are independent. But we are 
given that 

   P(bubbles) = 0.03  and  
   P(discoloured) = 0.05  and  
   P (both) = 0.01

But  0.03 x 0 .05 = 0.0015  NOT  0.01 and so the two events are not 
independent.

- Doctor Anthony, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Probability

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