(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A film is defective either when the level of sensitivity is wrong (defect D1) or when the colours are faulty (defect D2). 2% of all films made have at least one of these two defects. 1% of all films have defect D1 and 0.2% of all films have both defect D1 and D2.

Are the events "to have defect D1" and "to have defect D2" independent?

3. The attempt at a solution

P(D1) = 0.01

P(D1 ∩ D2) = 0.002

P(D1 ∪ D2) = 0.02

If independent, then: P(D1 ∪ D2) = P(D1) + P(D2) = 0.02

hence P(D2) = 0.02 - P(D1) = 0.02 - 0.01 = 0.01

P(D1 ∩ D2) = 0.01 x 0.01 = 0.0001 which is not 0.002

Is this correct? How do I prove that they are DEPENDENT, as all i have done is rejected their independency!

Thank you very much!

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# Homework Help: Probability - proving independence/dependence

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