GATE CSE
First time here? Checkout the FAQ!
x
+2 votes
456 views

Company X shipped 5 computer chips, 1 of which was defective. and company 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 Y?

  1. 2/9
  2. 4/9
  3. 2/3
  4. 1/2
asked in Probability by Veteran (76k points)   | 456 views
I think Option C is answer 2/3

4 Answers

+7 votes
Best answer

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

answered by Veteran (45k points)  
selected by
+1 vote

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

answered by Boss (9.6k points)  
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
answered by Junior (933 points)  
0 votes

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

 

answered by Veteran (52.4k points)  
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
yes but here we are choosing  any one from 9 -----------given in question
TWO SETS:BETWEEN 2 SET THE PROBABILITY OF BELONGING IS 1/2 OF EACH SET
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


Top Users Mar 2017
  1. rude

    4768 Points

  2. sh!va

    3054 Points

  3. Rahul Jain25

    2920 Points

  4. Kapil

    2728 Points

  5. Debashish Deka

    2602 Points

  6. 2018

    1574 Points

  7. Vignesh Sekar

    1422 Points

  8. Akriti sood

    1378 Points

  9. Bikram

    1342 Points

  10. Sanjay Sharma

    1126 Points

Monthly Topper: Rs. 500 gift card

21,517 questions
26,844 answers
61,157 comments
23,181 users