ISRO CSE 2007 | Question: 33

Question

Company $\text{X}$ shipped $5$ computer chips, $1$ of which was defective. and company $\text{Y}$ shipped $4$ computer chips, $2$ of which were defective. One computer chip is to be chosen uniformly at a 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 the company $\text{Y}?$

• A. $2/9$
• B. $4/9$
• C. $2/3$
• D. $1/2$

Comments

I think Option C is answer 2/3

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If the chosen chip is found to be defective, what is the probability that the chip came from the company Y?

Understanding this statement is VERY MUCH IMPORTANT 

if the choosen chip is found to be defective --> means, prior information given that chip is choosen and it is found to be defective

"what is the probability that chip came from company Y " --> it is

 P ( Y | defective) = P(Y, Defective) / P(Defective) 

if question asks --> if the choosen is from company Y , what is the probability that chip is defective ? 

then it is 

P(def | Y) = P(def , Y) / P(Y) = which is just a branch probability if you draw the tree diagram.

Answer 1

Using Bayesian probability theorem,

probability that a chip is shipped by company X = 5/9

probability that a chip is shipped by company Y = 4/9

probability of getting defective piece from company X = 1/5

probability of getting defective piece from company Y = 2/4

Hence, probability that  if the chosen chip is found to be defective,  then chip came from the company Y is

===> (4/9 * 2/4) / ((4/9 * 2/4) + (5/9 * 1/5))

===> 2/3 

Answer is C

Answer 2

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Ans C)

Answer 3

ANS IS 2/3.

1/2 IS THE PROBABILITY TO CHOOSE IN BETWEEN COMPANY X OR Y

APPLYING BAYS THEOREM

PROBABILITY=DEFECTIVE FROM COMPANY Y  /  DEFECTIVE FROM Y OR X

                      =(1/2*2/9)   ∕ [ (1/2*2/9)  +(1/2*1/9)]      (2/9=DEFECTIVE IN COMPANY Y AND 1/9 IS OF COMPANY X)

                      = 1/(1+(1/9*9/2)

                        = 1/(1+1/2) =1/(3/2)=2/3

ANS IS 2/3

Answer 4

My answer is not in option just check the logic

probablity of getting defective piece from company X = 1/5

probability of getting defective piece from company Y = 2/4

probability of getting Defective piece = 1/5 + 2/4

probability that the piece is from company Y = (2/4)/(1/5 + 2/4) = 5/7

Answer 5

We can choose any one from 9 chips =⁹C₁ ways

Now we are choosing defective one from company Y

Probability will be=²C₁ / ⁹C₁ =2/9

Comments

since there are 3 defective chips ( 1 from X  and 2 from Y) now chip is found to be defective(this is the given case and we dont need to find its prob) now it can belong to X or Y ) prob of belonging to X is 1/3 and that to Y is 2/3 as per my thinking

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yes but here we are choosing  any one from 9 -----------given in question

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TWO SETS:BETWEEN 2 SET THE PROBABILITY OF BELONGING IS 1/2 OF EACH SET

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it is the case of conditional prob. when one event has occured .language in question specifically says that drawn chip is found to be defective .now we just need to calculate that it belongs to Y or not . 2/9 ans would be when it were asked that what is the prob of finding a defective chip from company Y