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Consider a company that assembles computers. The probability of a faulty
 
Consider a company that assembles computers. The probability of a faulty
assembly of any computer is p. The company therefore subjects each
+
assembly of any computer is $p$. The company therefore subjects each
 
computer to a testing process. This testing process gives the correct result for
 
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
+
any computer with a probability of $q$. What is the probability of a computer
 
being declared faulty?
 
being declared faulty?
 
 
'''(A) pq + (1 - p)(1 - q)'''
+
'''(A) $pq + (1 - p)(1 - q)$'''
 
 
(B) (1 - q)p
+
(B) $(1 - q)p$
 
 
(C) (1 - q)p
+
(C) $(1 - q)p$
 
 
(D) pq
+
(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.
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[[Category: GATE2010]]
 
[[Category: GATE2010]]
 
[[Category: Probability questions]]
 
[[Category: Probability questions]]
[[Category:Mathematics Questions ]]
+
[[Category:Mathematics questions ]]

Revision as of 14:40, 29 June 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