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Consider a company that assembles computers. The probability of a faulty
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Consider a company that assembles computers. The probability of a faulty assembly of any computer is $p$. The company therefore subjects each computer to a testing process. This testing process gives the correct result for any computer with a probability of $q$. What is the probability of a computer being declared faulty?
assembly of any computer is p. The company therefore subjects each
 
computer to a testing process. This testing process gives the correct result for
 
any computer with a probability of q. What is the probability of a computer
 
being declared faulty?
 
 
 
'''(A) pq + (1 - p)(1 - q)'''
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'''(A) $pq + (1 - p)(1 - q)$'''
 
 
(B) (1 - q)p
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(B) $(1 - q)p$
 
 
(C) (1 - q)p
+
(C) $(1 - q)p$
 
 
(D) pq
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(D) $pq$
  
 
==={{Template:Author|Happy Mittal|{{mittalweb}} }}===
 
==={{Template:Author|Happy Mittal|{{mittalweb}} }}===
 
  P(declared faulty)  
 
  P(declared faulty)  
 
  = P(actually faulty)*P(declared faulty|actually faulty) +  P(not faulty)*P(declared faulty|not faulty)  
 
  = P(actually faulty)*P(declared faulty|actually faulty) +  P(not faulty)*P(declared faulty|not faulty)  
  = p*q + (1-p)*(1-q)
+
  = $p*q + (1-p)*(1-q)$
 
 
 
So, option <b>(A)</b> is correct.
 
So, option <b>(A)</b> is correct.
  
 
{{Template:FBD}}
 
{{Template:FBD}}
[[Category:Probability and Combinatorics]]
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[[Category: GATE2010]]
 
[[Category: GATE2010]]
[[Category: Probability questions]]
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[[Category: Probability questions from GATE]]
[[Category:Mathematics Questions from GATE]]
 

Latest revision as of 11:53, 15 July 2014

Consider a company that assembles computers. The probability of a faulty assembly of any computer is $p$. The company therefore subjects each computer to a testing process. This testing process gives the correct result for any computer with a probability of $q$. What is the probability of a computer being declared faulty?

(A) $pq + (1 - p)(1 - q)$

(B) $(1 - q)p$

(C) $(1 - q)p$

(D) $pq$

Solution by Happy Mittal

P(declared faulty) 
= P(actually faulty)*P(declared faulty|actually faulty) +  P(not faulty)*P(declared faulty|not faulty) 
= $p*q + (1-p)*(1-q)$

So, option (A) is correct.




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Consider a company that assembles computers. The probability of a faulty assembly of any computer is p. The company therefore subjects each computer to a testing process. This testing process gives the correct result for any computer with a probability of q. What is the probability of a computer being declared faulty?

(A) pq + (1 - p)(1 - q)

(B) (1 - q)p

(C) (1 - q)p

(D) pq

Solution by Happy Mittal[edit]

P(declared faulty) 
= P(actually faulty)*P(declared faulty|actually faulty) +  P(not faulty)*P(declared faulty|not faulty) 
= p*q + (1-p)*(1-q)

So, option (A) is correct.




blog comments powered by Disqus