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A wooden box contains exactly 12 nuts and 24 bolts. One-third of the bolts and one - third of the nuts are defective. If two items are picked from the box up one after the other without replacement, what is the probability that neither item is defective?
  • a)
    45/106
  • b)
    23/135
  • c)
    46/105
  • d)
    89/135
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A wooden box contains exactly 12 nuts and 24 bolts. One-third of the b...
Out of 12 nuts, 4 are defective while out of 24 bolts, 8 are defective.
So, there are 12 defective items and 24 non-defective items.
So, the probability that both items are non-defective (when picked without replacement one after the other)

Hence, option 3.
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Most Upvoted Answer
A wooden box contains exactly 12 nuts and 24 bolts. One-third of the b...
Given information:
- The box contains 12 nuts and 24 bolts.
- One-third of the nuts (12/3 = 4) and one-third of the bolts (24/3 = 8) are defective.

To find: The probability that neither item picked is defective.

Approach:
- To solve this problem, we can use the concept of combinations and probability.
- The probability of picking a non-defective nut from the box is (12 - 4) / 36 = 8/36.
- The probability of picking a non-defective bolt from the box is (24 - 8) / 36 = 16/36.
- Since the items are picked without replacement, the probability of picking two non-defective items in succession can be found by multiplying the probabilities.
- Hence, the required probability is (8/36) * (16/36).

Calculation:
To simplify the calculation, we can divide both the numerator and denominator by 4.
- The required probability becomes (2/9) * (4/9).
- Multiplying the numerators and denominators, we get 8/81.

Simplifying further, we can divide both the numerator and denominator by 8.
- The required probability becomes 1/9.

Therefore, the probability that neither item picked is defective is 1/9.

Answer:
The correct answer is option C) 46/105.
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