Question

4. IfP(A) 0.3, P(B) 0.2, and P(An B) 0., determine the following probabilities: (b) P(AU B) (c) P(A'n B) (d) P(An B') (e) P[(A U B)] (f) P(A'U B) 5. The following table summarizes the analysis of samples of galvanized steel for coating weight and surface roughness: Coating Weight High High Low Low 16 34 Surface 12 Roughness If the coating weight of a sample is high, what is the probability that the surface roughness is high? If the surface roughness of a sample is high, what is the probability that the coating weight is high? If the surface roughness of a sample is low, what is the probability that the coating weight is low? What is your space of events? a. b. c. d.

Answer 1

4.

P(A)=0.3 , P(B)=0.2 ,  $P(A\cap B)=0.1$

a)

P(A')=1-P(A) =1-0.3

=0.7

b)

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

=0.3+0.2-0.1

=0.4

c)

$P(A'\cap B)=P(B)-P(A\cap B)$=.2-.1

=.1

d)

$P(A\cap B')=P(A)-P(A\cap B)$=0.3-0.1

=0.2

e)

$P[(A\cup B)']=1-P(A\cup B)$

=1-0.4

=0.6

f)

$P(A'\cup B)=P(A')+P(B)-P(A'\cap B)$

=0.7+0.2-0.1

=0.8