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To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample without replacement. If either bulb is defective, the entire lot is rejected. suppose a sample of 200 bulbs contains 5 defective bulbs. Find the probability that the sample will be rejected.
- a)294/1170
- b)197/3980
- c)58/157
- d)168/267
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
To test the quality of electric bulbs produced in a factory, two bulbs...
clearly the sample will be rejected if at least one of the two bulbs is defective .
therefore ,if we consider the following event :
A=First bulbs is defective ,B = second bulbs is defective then,
Required probability = P(A ∪ B)
therefore ,if we consider the following event :
A=First bulbs is defective ,B = second bulbs is defective then,
Required probability = P(A ∪ B)
Most Upvoted Answer
To test the quality of electric bulbs produced in a factory, two bulbs...
Calculation:
To find the probability that the sample will be rejected, we need to consider the probability of selecting at least one defective bulb in the sample.
Total number of bulbs in the sample (N):
N = 200
Number of defective bulbs in the sample (D):
D = 5
Probability of selecting a defective bulb in the first draw:
P(defective at first draw) = D/N = 5/200 = 1/40
Probability of selecting a non-defective bulb in the first draw:
P(non-defective at first draw) = 1 - P(defective at first draw) = 1 - 1/40 = 39/40
Probability of selecting a non-defective bulb in the first draw and second draw:
P(non-defective at first draw and second draw) = (39/40) * (38/39) = 38/40 = 19/20
Probability of rejecting the sample:
P(reject) = 1 - P(non-defective at first draw and second draw) = 1 - 19/20 = 1/20
Therefore, the probability that the sample will be rejected is 1/20, which is equivalent to 197/3980. Hence, the correct answer is option B) 197/3980.
To find the probability that the sample will be rejected, we need to consider the probability of selecting at least one defective bulb in the sample.
Total number of bulbs in the sample (N):
N = 200
Number of defective bulbs in the sample (D):
D = 5
Probability of selecting a defective bulb in the first draw:
P(defective at first draw) = D/N = 5/200 = 1/40
Probability of selecting a non-defective bulb in the first draw:
P(non-defective at first draw) = 1 - P(defective at first draw) = 1 - 1/40 = 39/40
Probability of selecting a non-defective bulb in the first draw and second draw:
P(non-defective at first draw and second draw) = (39/40) * (38/39) = 38/40 = 19/20
Probability of rejecting the sample:
P(reject) = 1 - P(non-defective at first draw and second draw) = 1 - 19/20 = 1/20
Therefore, the probability that the sample will be rejected is 1/20, which is equivalent to 197/3980. Hence, the correct answer is option B) 197/3980.
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To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample without replacement. If either bulb is defective, the entire lot is rejected. suppose a sample of 200 bulbs contains 5 defective bulbs. Find the probability that the sample will be rejected.a)294/1170b)197/3980c)58/157d)168/267Correct answer is option 'B'. Can you explain this answer?
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