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A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch
is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs.
The probability that the current batch is accepted is _________
is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs.
The probability that the current batch is accepted is _________
(Important - Enter only the numerical value in the answer)
Correct answer is '0.8145'. Can you explain this answer?
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Question: A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs. The probability that the current batch is accepted is _________ (Important - Enter only the numerical value in the answer).
Answer:
To find the probability that the current batch is accepted, we need to calculate the probability that all four randomly chosen bulbs are non-defective.
Step 1: Finding the probability of selecting a non-defective bulb in the first attempt
Since there are 100 bulbs in the batch and five of them are defective, the probability of selecting a non-defective bulb in the first attempt is:
P(non-defective on first attempt) = (100 - 5) / 100 = 95 / 100 = 0.95
Step 2: Finding the probability of selecting a non-defective bulb in the second attempt
After the first non-defective bulb has been selected, there are 99 bulbs remaining in the batch, out of which four are defective. So, the probability of selecting a non-defective bulb in the second attempt is:
P(non-defective on second attempt) = (99 - 4) / 99 = 95 / 99 ≈ 0.9596
Step 3: Finding the probability of selecting a non-defective bulb in the third attempt
After the second non-defective bulb has been selected, there are 98 bulbs remaining in the batch, out of which three are defective. So, the probability of selecting a non-defective bulb in the third attempt is:
P(non-defective on third attempt) = (98 - 3) / 98 = 95 / 98 ≈ 0.9694
Step 4: Finding the probability of selecting a non-defective bulb in the fourth attempt
After the third non-defective bulb has been selected, there are 97 bulbs remaining in the batch, out of which two are defective. So, the probability of selecting a non-defective bulb in the fourth attempt is:
P(non-defective on fourth attempt) = (97 - 2) / 97 = 95 / 97 ≈ 0.9794
Step 5: Calculating the probability of the current batch being accepted
To calculate the probability that all four randomly chosen bulbs are non-defective, we multiply the probabilities from each step together:
P(batch accepted) = P(non-defective on first attempt) * P(non-defective on second attempt) * P(non-defective on third attempt) * P(non-defective on fourth attempt)
P(batch accepted) ≈ 0.95 * 0.9596 * 0.9694 * 0.9794 ≈ 0.8145
Therefore, the probability that the current batch is accepted is approximately 0.8145.
Answer:
To find the probability that the current batch is accepted, we need to calculate the probability that all four randomly chosen bulbs are non-defective.
Step 1: Finding the probability of selecting a non-defective bulb in the first attempt
Since there are 100 bulbs in the batch and five of them are defective, the probability of selecting a non-defective bulb in the first attempt is:
P(non-defective on first attempt) = (100 - 5) / 100 = 95 / 100 = 0.95
Step 2: Finding the probability of selecting a non-defective bulb in the second attempt
After the first non-defective bulb has been selected, there are 99 bulbs remaining in the batch, out of which four are defective. So, the probability of selecting a non-defective bulb in the second attempt is:
P(non-defective on second attempt) = (99 - 4) / 99 = 95 / 99 ≈ 0.9596
Step 3: Finding the probability of selecting a non-defective bulb in the third attempt
After the second non-defective bulb has been selected, there are 98 bulbs remaining in the batch, out of which three are defective. So, the probability of selecting a non-defective bulb in the third attempt is:
P(non-defective on third attempt) = (98 - 3) / 98 = 95 / 98 ≈ 0.9694
Step 4: Finding the probability of selecting a non-defective bulb in the fourth attempt
After the third non-defective bulb has been selected, there are 97 bulbs remaining in the batch, out of which two are defective. So, the probability of selecting a non-defective bulb in the fourth attempt is:
P(non-defective on fourth attempt) = (97 - 2) / 97 = 95 / 97 ≈ 0.9794
Step 5: Calculating the probability of the current batch being accepted
To calculate the probability that all four randomly chosen bulbs are non-defective, we multiply the probabilities from each step together:
P(batch accepted) = P(non-defective on first attempt) * P(non-defective on second attempt) * P(non-defective on third attempt) * P(non-defective on fourth attempt)
P(batch accepted) ≈ 0.95 * 0.9596 * 0.9694 * 0.9794 ≈ 0.8145
Therefore, the probability that the current batch is accepted is approximately 0.8145.
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A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batchis rejected if even one of the bulbs is defective. A batch typically has five defective bulbs.The probability that the current batch is accepted is _________(Important - Enter only the numerical value in the answer)Correct answer is '0.8145'. Can you explain this answer?
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A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batchis rejected if even one of the bulbs is defective. A batch typically has five defective bulbs.The probability that the current batch is accepted is _________(Important - Enter only the numerical value in the answer)Correct answer is '0.8145'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batchis rejected if even one of the bulbs is defective. A batch typically has five defective bulbs.The probability that the current batch is accepted is _________(Important - Enter only the numerical value in the answer)Correct answer is '0.8145'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batchis rejected if even one of the bulbs is defective. A batch typically has five defective bulbs.The probability that the current batch is accepted is _________(Important - Enter only the numerical value in the answer)Correct answer is '0.8145'. Can you explain this answer?.
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