SOLUTION: 37. A box is filled with 12 locks of which 4 are defective. All the locks look alike and have equal probability of being defective. 3 locks are chosen and placed in a box. What is

Algebra ->  Probability-and-statistics -> SOLUTION: 37. A box is filled with 12 locks of which 4 are defective. All the locks look alike and have equal probability of being defective. 3 locks are chosen and placed in a box. What is      Log On


   

Question 875430: 37. A box is filled with 12 locks of which 4 are defective. All the locks look alike and have equal probability of
being defective. 3 locks are chosen and placed in a box. What is the probability that 2 locks are defective?
Found 2 solutions by jim_thompson5910, bond:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
There are 12 C 3 = 220 ways to pick 3 locks from the pool of 12.

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There are 4 defective locks.

There are 12-4 = 8 non-defective locks.

There are (4 C 2)*(8 C 1) = (6)*(8) = 48 ways to pick 3 locks where 2 are defective and 1 is non-defective.

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Probability: (# of ways to pick 3 locks with 2 defective)/(# of ways total) = 48/220 = 12/55

Answer by bond(4) About Me  (Show Source):
You can put this solution on YOUR website!
The probability of 2 defective among 3 chosen is = 4/12 * 3/11 * 8/10
This can done in 3 ways hence = 3 * 4/12 * 3/11 * 8/10 = 12 /55.