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October 10th, 2013, 05:02 AM   #1
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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.
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October 10th, 2013, 08:01 AM   #2
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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.)
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October 10th, 2013, 09:06 AM   #3
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Re: An electronics assembly consists of two independent sub

Quote:
Originally Posted by r-soy
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.
There are two things wrong with this question:

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).
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October 11th, 2013, 10:56 PM   #4
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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?
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October 11th, 2013, 11:39 PM   #5
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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.
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October 12th, 2013, 12:08 AM   #6
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Re: An electronics assembly consists of two independent sub

Thanks so so much.
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October 15th, 2013, 12:02 AM   #7
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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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