A factory produces light bulbs. It is known that 7% of the bulbs produced are defective. Bulbs are packed in boxes of 12.
(a) Find the probability that a randomly selected box contains exactly one defective bulb. [3]
(b) Find the probability that a randomly selected box contains at least two defective bulbs. [2]
(c) A quality inspector selects 10 boxes at random. Find the probability that exactly 3 of these boxes contain at least two defective bulbs. [2]
Question
Find the probability that a randomly selected box contains exactly one defective bulb. [3]
Hint
Hint
Hint
Apply the binomial formula: P(D = 1) = (12 choose 1) × (0.07)^1 × (0.93)^(11).
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Answer
Answer
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Explanation
Explanation
Complete Answer
Approximately 0.378
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Question
Find the probability that a randomly selected box contains at least two defective bulbs. [2]
Hint
Hint
Hint
Use the complement rule: P(D ≥ 2) = 1 − [P(D = 0) + P(D = 1)].
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Answer
Answer
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Explanation
Explanation
Complete Answer
Approximately 0.202
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Question
A quality inspector selects 10 boxes at random. Find the probability that exactly 3 of these boxes contain at least two defective bulbs. [2]
Hint
Hint
Hint
Let X be the number of boxes (out of 10) with at least two defective bulbs. Then, X ∼ Binomial(10, 0.202). Compute P(X = 3) = (10 choose 3) × (0.202)^3 × (0.798)^7.
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Answer
Answer
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Explanation
Explanation
Complete Answer
Approximately 0.203
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