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8) In a production line of a factory, each packet contains four items. Past record shows that 20% of the produced items are defective. A quality manager inspects each item in a packet and approves the packet for shipment if at most one item in the packet is found to be defective. Then what is the probability (round off?
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8) In a production line of a factory, each packet contains four items....
First, we need to calculate the probability of having at most one defective item in a packet.
- Calculating the probability of having exactly one defective item:
- The probability of having exactly one defective item in a packet of four items can be calculated using the binomial probability formula:
- P(X = 1) = C(4, 1) * (0.2)^1 * (0.8)^3
- P(X = 1) = 4 * 0.2 * 0.8^3
- P(X = 1) = 0.4096
- Calculating the probability of having zero defective items:
- The probability of having zero defective items in a packet can be calculated using the binomial probability formula:
- P(X = 0) = (0.8)^4
- P(X = 0) = 0.4096
- Calculating the total probability:
- The total probability of having at most one defective item in a packet is the sum of the probabilities of having exactly one or zero defective items:
- P(at most one defective) = P(X = 0) + P(X = 1)
- P(at most one defective) = 0.4096 + 0.4096
- P(at most one defective) = 0.8192
Therefore, the probability of a packet being approved for shipment is 0.8192 or 81.92%.
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8) In a production line of a factory, each packet contains four items. Past record shows that 20% of the produced items are defective. A quality manager inspects each item in a packet and approves the packet for shipment if at most one item in the packet is found to be defective. Then what is the probability (round off?
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