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October 10th, 2013, 05:02 AM  #1 
Senior Member Joined: Oct 2009 Posts: 895 Thanks: 1  An electronics assembly consists of two independent sub syst
1) An electronics assembly consists of two independent sub systems A and B > From previous testing procedures, the following probabilities are known p(A fails) = 0.2 , p(B fails) = 0.19 , P(A fails or B fails) = 0.18 Find the probability that both A and B fail. 2) The probability that a student owns a car is .65 and the probability that a student owns a computer is .82. If the probability that a student owns both is .55, what is the probability that both A and B fail? 3) A box contain 4 bad 6 good tubes. Two are drawn from the box at a time. What is the probability that both tubes drawn are good? Please can help me to solve this question. I need clear out the answer with explanation. 
October 10th, 2013, 08:01 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,711 Thanks: 1805 
1) P(A fails & B fails) = P(A fails) + P(B fails)  P(A fails or B fails) = 0.2 + 0.19  0.18 = 0.21. 2) You have typed the question incorrectly, as A and B have not been defined. P(student owns a car or computer) = 0.65 + 0.82  0.55 = 0.92. 3) If each tube available is equally likely to be drawn and two distinct tubes are drawn, the required probability = (6/(6+4))(5/(5+4)) = 1/3. (When first is chosen, 6 of 10 are good. After a good tube has been drawn, 5 good tubes remain amongst the 9 still available to be drawn.) 
October 10th, 2013, 09:06 AM  #3  
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: An electronics assembly consists of two independent sub Quote:
1) If A and B are independent, then P(A and B) = P(A)P(B) and P(A or B) = P(A) + P(B)  P(A)P(B). 2) In any case, P(A or B) cannot be less than P(A) or P(B).  
October 11th, 2013, 10:56 PM  #4 
Senior Member Joined: Oct 2009 Posts: 895 Thanks: 1  Re: An electronics assembly consists of two independent sub
2) The probability that a student owns a car is .65 and the probability that a student owns a computer is .82. If the probability that a student owns both is .55 what is the probability that a given student owns neither a car nor a computer? What does that mean (what is the probability that given student owns neither a car nor a computer) and what is the formula here ... and what if here written either instead of neither? 
October 11th, 2013, 11:39 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 19,711 Thanks: 1805 
The question "what is the probability that a given student owns neither a car nor a computer" means "what is the probability that a given student does not own a car and does not own a computer". The question would be ungrammatical if "neither" were changed to "either". P(student does not own a car and does not own a computer) = 1  P(student owns a car or a computer) = 1  0.92 = 0.08. 
October 12th, 2013, 12:08 AM  #6 
Senior Member Joined: Oct 2009 Posts: 895 Thanks: 1  Re: An electronics assembly consists of two independent sub
Thanks so so much.

October 15th, 2013, 12:02 AM  #7 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: An electronics assembly consists of two independent sub
Another way to think about it is to consider a typical 100 students: 55 own both a car and a computer Another 10 own a car (but no computer) (making 65 in all who own a car) Another 27 own a computer (but no car) (making 82 in all who one a computer) Leaving 8 who own neither. 

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