A firm has ordered a batch of identical electronic device from 4 different suppl

Question

A firm has ordered a batch of identical electronic device from 4 different suppliers with the following distribution: 30% supplier 1, 20% supplier 2, 35% supplier 3, and 15% supplier 4. The historical data shows that 8% of supplier 1 items, 6% of supplier 2 items, 4% of supplier 3 items, and 10% of supplier 4 items are defective. What is the probability that a randomly selected device is coming from supplier 3 and is defective? If an item is selected randomly from the batch, what is the probability that the selected item is defective? If an item is selected at random and it is defective, what is the probability that it is coming from supplier 3?

Explanation / Answer

Let total number of identical electronic device be 100%.

Contribution of identical electronic device to different suppliers are as follows :-

Supplier 1 = 30 % ; Supplier 2 = 20 % ; Supplier 3 = 35 % ; Supplier 4 = 15 %

Total = 100 %

Of 30 % supplier 1 percentage of defective devices = 8 %

Therefore contribution of defective devices from supplier 1 in total defective devices = 8 % of 30 %

= 2.4 % of total devices

Similarly,

Of 20 % supplier 2 percentage of defective devices = 6 %

Therefore contribution of defective devices from supplier 1 in total defective devices = 6 % of 20 %

= 1.2 % of total devices

Of 35 % supplier 3 percentage of defective devices = 4 %

Therefore contribution of defective devices from supplier 3 in total defective devices = 4 % of 35 %

= 1.4 % of total devices

Of 15 % supplier 4 percentage of defective devices = 10 %

Therefore contribution of defective devices from supplier 4 in total defective devices = 10 % of 15 %

= 1.5 % of total devices

So, the total defective devices = Defective devices of supplier 1 + Defective devices of supplier 2 + Defective devices of supplier 3 + Defective devices of supplier 4

= 2.4 % + 1.2 % + 1.4 % + 1.5 %

= 6.5 %

1)

The probability that a randomly selected device is coming from supplier 3 and is defective

= Probability of selecting a device from supplier 3 and is defective

Probability of selecting a device

= 1.4 % / 100 %

= 1.4 / 100

= 14 / 1000

= 0.014

2)

Probability that a selected item is defective

= Probability of a defective device

Probability of selecting a device

= 6.5 % / 100 %

= 65 / 1000

= 0.065

3)

The probability that a randomly selected device is defective given that it is coming from Supplier 3

= P(Supplier 3 and Defective) / P(Defective)

= 1.4 % / 6.5 %

= 14 / 65

= 0.2154

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