Question 1151388
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I don't know what is the source of this problem,  who created it and where is it came from,


but the assumption that the events  P  and  S  are independent  CONTRADICTS  to the rest of the post.



The situation described in the post,  NEVER  may happen,  and in this sense,  the problem is  DEFECTIVE 
(= <U>is fake problem</U>, &nbsp;in simple terms).


So, if you want to have a correctly posed problem, &nbsp;take off this assumption that the events &nbsp;P &nbsp;and &nbsp;S &nbsp;are independent.



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And be careful in creating problems, when and if you don't know the subject and the terminology . . .