Mathematics: In the manufacturing of a chemical adhesive, 3% of all batches have raw materials from two different lots. this occurs when holding tanks are replenished and the remaining portion of a lot is insufficient to fill the tanks. only 5% of batches with material from a single lot require reprocessing. however, the viscosity of batches consisting of two or more lots of material is more difficult to control, and 40% of such batches require additional processing to achieve the required viscosity. let a denote

In the manufacturing of a chemical adhesive, 3%

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02.01.2022

Step-by-step explanation:

By the problem we know that our events are:

A batch is formed from two different lots.

A batch requires additional processing.

So, according to that:

a) P(A)=3%=0.03

Because P(A) and $P(A^{'} )$ are complementary events

b) $P(A^{'} )=1-P(A)=1-0.03=0.97=97%$

Because of the problem, we know that:

c) P(B/A)=0.4=40%

and,

d) $P(B/A^{'} )=0.05=5%$

From the formula

e) P(A ∩ B)= P(A)*P(B/A)= (0.03)*(0.4)=0.012

f) P(A ∩ B')=P(A)-P(A ∩ B)= 0.03-0.012=0.018

And, finally

g) P(B)=P(B/A)*P(A)+P(B/A')*P(A')= (0.4)*(0.03)+(0.05)(0.97)=0.0605

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