Conduct an experiment with two systems producing the same type of product. The first system produces 300 products with 291 of them being qualified. The second system produces 400 products with 392 of them being qualified.
a) Calculate the probability of producing a defective product for each system.
b) Suppose each system produces one product independently at the same time. Calculate the probability that exactly one of the products is qualified.

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reinhard10158 reinhard10158 · Answer 1 · 2024-07-25T04:41:29-04:00

Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

a)

totally possible cases of system A : 300

"desired" (defect) cases of system A : 300 - 291 = 9

totally possible cases of system B : 400

"desired" (defect) cases of system B : 400 - 392 = 8

the probability of creating a defective product in A is

9/300 = 3/100 = 0.03

the probabilty of creating a defective product in B is

8/400 = 2/100 = 0.02

b)

exactly one of the 2 products is qualified.

so, either the one of A is qualified and the one of B is defective, or the one of B is qualified and the one of A is defective.

independent "and" relations are expressed as multiplications of the individual events.

exclusive "or" relations are expressed as summary of the individual events.

so, in our case

the probability of a qualified product in A is

291/300 = 97/100 = 0.97

the probability of a qualified product in B is

392/400 = 98/100 = 0.98

and the combined probability is

0.97×0.02 + 0.98×0.03 = 0.0488