There are 500 packets in a large box and each packet contains 4 electric devices in it- On testing- at the time of packing- it was noted that there are some faulty pieces in the packets- The data is as given below - No of faulty devices in a packet 0 1 2 3 4 Total number of packets- Number of packets 300 100 50 30 20 500- -i If a buyer will only tolerate the maximum of one faulty piece in a packet- what is the probability that a packet will be rejected by him-ii Another buyer will only take packets with all the pieces functional- What is the probability that a packet will be rejected- -4 MARKS-

Concept: I Mark Solution: 1.5 Marks each Packets with more than one nbsp;defective piece = 50 + 30 + 20 nbsp;= 100 (i) Probability that the first buyer wi ...

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Standard X

Mathematics

Complementary Event

There are 500...

Question

There are 500 packets in a large box and each packet contains 4 electric devices in it. On testing, at the time of packing, it was noted that there are some faulty pieces in the packets. The data is as given below :

$\begin{matrix} No of faulty devices in a packet & 0 & 1 & 2 & 3 & 4 & Total number of packets Number of packets & 300 & 100 & 50 & 30 & 20 & 500 \end{matrix}$

(i) If a buyer will only tolerate the maximum of one faulty piece in a packet, what is the probability that a packet will be rejected by him?

(ii) Another buyer will only take packets with all the pieces functional. What is the probability that a packet will be rejected? [4 MARKS]

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Solution

Concept: I Mark
Solution: 1.5 Marks each

Packets with more than one defective piece = 50 + 30 + 20 = 100

(i) Probability that the first buyer will reject a packet
$= \frac{100}{500} = 0.2$

Packets with no defective piece = 300
Packets with at least 1 defective piece = 500-300 = 200

(ii) Probability that the second buyer will reject a packet = $= \frac{200}{500} = 0.4$

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