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From a box containing a dozen bulbs, of which exactly half of them are good, four bulbs are choosen at random and fitted into the four bulb holders in a room. The probability that the room gets lighted is
  • a)
    2/3
  • b)
    33/44
  • c)
    32/33
  • d)
    1/33
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
From a box containing a dozen bulbs, of which exactly half of them are...
Since [x  π] is an integer for all x, therefore π [x  π] is an integral multiple of π for all x.Hence tan (π[x  π]) = 0 for all x. Also 1 + [x]2 ≠ 0 for all x. 
Therefore f (x) = 0 for all x.
Hence f (x) is continuous and derivable at all x.
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Most Upvoted Answer
From a box containing a dozen bulbs, of which exactly half of them are...
Probability of the room getting lighted:

Given:
- Total number of bulbs = 12
- Number of good bulbs = 6
- Bulbs chosen at random = 4

Finding the probability:
- Total ways to choose 4 bulbs out of 12 = 12C4 = 495
- Number of ways to choose 4 good bulbs out of 6 = 6C4 = 15
- Number of ways to choose 4 bulbs with at least 1 good bulb = 495 - 6C4 = 480

Probability = Number of favorable outcomes / Total outcomes
- Probability of the room getting lighted = 480 / 495
- Probability of the room getting lighted = 32/33
Therefore, the correct answer is option C) 32/33.
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From a box containing a dozen bulbs, of which exactly half of them are good, four bulbs are choosen at random and fitted into the four bulb holders in a room. The probability that the room gets lighted isa)2/3b)33/44c)32/33d)1/33Correct answer is option 'C'. Can you explain this answer?
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