desmond iking
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Probability of independent events
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Set A should be the set of all products with defect A
Similarly for set B.
Now can you see why the sets intersect?
What does that look like on a venn diagram? (hint: not like you did).
Independent events are those whose probability is not affected by the occurrence of the other.
i.e. where P(A|B)=P(A), P(B|A)=P(B)
Since: P(A|B)=P(AnB)/P(B)
This means that for independent events, P(AnB)=P(A)P(B).
(using AnB = "A intersection B")
Similarly for set B.
Now can you see why the sets intersect?
What does that look like on a venn diagram? (hint: not like you did).
Independent events are those whose probability is not affected by the occurrence of the other.
i.e. where P(A|B)=P(A), P(B|A)=P(B)
Since: P(A|B)=P(AnB)/P(B)
This means that for independent events, P(AnB)=P(A)P(B).
(using AnB = "A intersection B")
desmond iking
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desmond iking said:
Correct. Do you see now why your answer was wrong? You essentially did the following:
[tex]\mathbb{P}(A\cup B) = \mathbb{P}(A) + \mathbb{P}(B)[/tex]
which is only allowed if ##A## and ##B## do not intersect. But ##A## and ##B## do intersect here, so you cannot apply this formula!
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To be a little more specific about independent events -- If events A and B are independent, the probability of event A happening is the same whether B occurs or not. And the converse is true. One way to show that in a Venn diagram is to draw A as a horizontal slice of the whole diagram, and B as a vertical slice of the whole diagram. That way the percent of A within B is the same as the percent of A within the entire diagram (and vice versa). The first diagram in the attachment shows independent events and the second diagram shows dependent events
