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There are 25 calculators in a box. Two of them are defective. Suppose 5 calculators are randomly picked for inspection (i.e., each has the same chance of being selected), what is the probability that only one of the defective calculators will be included in the inspection?
  • a)
    1/2
  • b)
    1/3
  • c)
    1/4
  • d)
    1/5
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
There are 25 calculators in a box. Two of them are defective. Suppose ...
To arrive at the answer, first note that there are C(2,1) = 2 ways to choose one defective calculator out of the 2 available.
Next, there are C(23,4) ways to choose 4 non-defective calculators from the 23 good ones.
Since the total number of ways to pick any 5 calculators from 25 is C(25,5),
the probability that exactly one defective calculator is chosen is given by [C(2,1) × C(23,4)] / C(25,5).
the probability simplifies to 1/3.
 
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