IIT JEE , AIEEE Forum - Mathematics , Algebra - Company X shipped 5 computer chips,1 of which is defective and Company Y shipped 4 compute

sneha.bagri

Company X shipped 5 computer chips,1 of which is defective and Company Y shipped 4 computer chips, 2 of which were defective. One computer chip is to be choosen uniformly at random from the 9 chips shipped by the companies. If the chosen chip is found to be defective, what is the probability that the chip came from company y?

allamraju

The ans is 5/7.It is based on bayes theorem.Is it correct and do u want me to post the complete soln.

sneha.bagri

ya but here the options given are
1)2/9
2) 4/9
3)1/2
4)2/3

allamraju

Oh..I made a silly mistake.The ans is 2/3

P(Y/D)=P(Y).P(D/Y)/P(X).P(D/X)+P(Y).P(D/Y)=(4/9.1/2)/(4/9.1/2+5/9.1/5)=2/3

mukundmadhav

How so? It should be 1/3
(4/9).(1/2) + (5/9)(1/5)

mukundmadhav

Wait that's wrong sorry
That's the probability that it is defective.
Defective chip from complany Y probability is 1/2.4/9 = 2/9
So probability is (2/9)/(1/3) = 2/3
Sorry allamraju :D

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The ans is 5/7.It is based on bayes theorem.Is it correct and do u want me to post the complete soln.

Oh..I made a silly mistake.The ans is 2/3

P(Y/D)=P(Y).P(D/Y)/P(X).P(D/X)+P(Y).P(D/Y)=(4/9.1/2)/(4/9.1/2+5/9.1/5)=2/3