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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 $\text{Y}?$

  1. $2/9$
  2. $4/9$
  3. $2/3$
  4. $1/2$
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5 Answers

Best answer
18 votes
18 votes

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

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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

0 votes
0 votes
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:

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