Homework Soursea firm has orderd a batch of identical electronic devices fr
a firm has orderd a batch of identical electronic devices 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.
1- what is the probability that a randomly selected device is coming from supplier 3 and is defective?
2- if an item is selected randomly from the batch, what is the probability that the selected item is defective?
3- if an item is selected at random and it is defective, what is the probability that it is coming from supplier 3 ?
a firm has orderd a batch of identical electronic devices 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.
1- what is the probability that a randomly selected device is coming from supplier 3 and is defective?
2- if an item is selected randomly from the batch, what is the probability that the selected item is defective?
3- if an item is selected at random and it is defective, what is the probability that it is coming from supplier 3 ?
a firm has orderd a batch of identical electronic devices 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.
1- what is the probability that a randomly selected device is coming from supplier 3 and is defective?
2- if an item is selected randomly from the batch, what is the probability that the selected item is defective?
3- if an item is selected at random and it is defective, what is the probability that it is coming from supplier 3 ?
Solution
The above table gives a clear picture of proporiton of prob for defectives from different suppliers
1) probability that a randomly selected device is coming from supplier 3 and is defective = 0.015
2) an item is selected randomly from the batch, what is the probability that the selected item is defective
= Prob for defective =
0.085
3) if an item is selected at random and it is defective, what is the probability that it is coming from supplier 3
= P(supplier 3 and defective)/Prob defective
= 0.015/0.085
= 0.1765
| Supplier | I | II | III | IV | Total |
| Percent of distribution | 30 | 20 | 35 | 15 | 100 |
| Defective percent | 8 | 6 | 4 | 10 | |
| Prob of defective(in decimals) | 0.024 | 0.012 | 0.014 | 0.015 | 0.085 |
