Bubbles in the GlassDate: 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/ |
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