Question

themanufactur go, a chemical ad esive, 6%ofa insufficient to fill the tanks. bate es hve raw n eas twan eile,mi oan he knete neemd ii m torm need Only 5% of batches with material from a single lot require reprocessing. However, the batches require additional processing to achieve the required viscosity. scosity of batches eonsisting or two or more i s o, me ears more amak to anos, naan, p' i。 Let A denote the event that a batch is formed from two dfferent lots, and let 8 denote the event that a lot requires additional processing. Determine the following probabities. Round your answers to three decimal places (e.g. 98.765) o) P(A) e) PBA) P(aA) (e) P(A n 8)- (f) P(Ana).

Answer 1

a)P(A)=0.06

b)P(A')=1-P(A)=1-0.06=0.94

c)P(B|A)=0.05

d)P(B|A')=0.40

e)P(A n B)=P(A)*P(B|A)=0.06*0.05=0.003

f)P(A n B')=P(A)-P(A n B)=0.06-0.003=0.057

g)P(B)=P(A)*P(B|A)+P(A')*P(B|A')=0.06*0.05+0.94*0.40=0.379