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A box contains 30 electric bulbs, out of which 8 are defective. Four bulbs are chosen at random from this box. Find the probability that at least one of them is defective?
- a)432/783
- b)574/783
- c)209/784
- d)334/784
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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A box contains 30 electric bulbs, out of which 8 are defective. Four b...
1 – 22c4/30c4 = 1 – 209/783 = 574/783
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A box contains 30 electric bulbs, out of which 8 are defective. Four b...
To find the probability that at least one of the four bulbs chosen is defective, we can use the concept of complementary probability.
The total number of ways to choose 4 bulbs out of 30 is given by the combination formula:
C(30, 4) = 30! / (4! * (30-4)!) = 27,405
Now, let's calculate the probability that none of the four bulbs chosen is defective.
The number of ways to choose 4 bulbs out of the 22 non-defective bulbs is given by the combination formula:
C(22, 4) = 22! / (4! * (22-4)!) = 7,015
Therefore, the probability of choosing 4 non-defective bulbs is:
P(4 non-defective bulbs) = 7,015 / 27,405
Now, we can find the probability that at least one of the four bulbs chosen is defective by subtracting the probability of choosing 4 non-defective bulbs from 1:
P(at least one defective bulb) = 1 - P(4 non-defective bulbs)
= 1 - 7,015 / 27,405
= (27,405 - 7,015) / 27,405
= 20,390 / 27,405
= 574 / 783
Therefore, the correct answer is option B) 574/783.
The total number of ways to choose 4 bulbs out of 30 is given by the combination formula:
C(30, 4) = 30! / (4! * (30-4)!) = 27,405
Now, let's calculate the probability that none of the four bulbs chosen is defective.
The number of ways to choose 4 bulbs out of the 22 non-defective bulbs is given by the combination formula:
C(22, 4) = 22! / (4! * (22-4)!) = 7,015
Therefore, the probability of choosing 4 non-defective bulbs is:
P(4 non-defective bulbs) = 7,015 / 27,405
Now, we can find the probability that at least one of the four bulbs chosen is defective by subtracting the probability of choosing 4 non-defective bulbs from 1:
P(at least one defective bulb) = 1 - P(4 non-defective bulbs)
= 1 - 7,015 / 27,405
= (27,405 - 7,015) / 27,405
= 20,390 / 27,405
= 574 / 783
Therefore, the correct answer is option B) 574/783.
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