Answer:
a)
0.5
option A
b)
0.6
c)
0.1
Step-by-step explanation:
The event A and B are independent so
P(A∩B)=P(A)*P(B)
P(A∩B)=P(0.2)*P(0.5)=0.10
a)
We have to find P(B'|A')
P(B'|A')=P(B'∩A')/P(A')
P(A)=0.2
P(A')=Asian project is not successful=1-P(A)=1-0.2=0.8
P(B)=0.5
P(B')=Europe project is not successful=1-P(B)=1-0.5=0.5
P(B'∩A')=Europe and Asia both project are not successful=P(A')*P(B')=0.8*0.5=0.4
P(B'|A')=P(B'∩A')/P(A')=0.4/0.8=0.5
This can be done by another independence property for conditional probability
P(B|A)=P(B)
P(B'|A')=P(B')
P(B'|A')=0.5
b)
Probability of at least one of two projects will be successful means that the probability of success of Asia project or probability of success of Europe project or probability of success of Europe and Asian project which is P(AUB).
P(AUB)=P(A)+P(B)-P(A∩B)
P(AUB)=0.2+0.5-0.1
P(AUB)=0.6
c)
Probability of only Asian project is successful given that at least one of the two projects is successful means that probability of success of project Asia while the project Europe is not successful denoted as P((A∩B')/(A∪B))=?
P((A∩B')/(A∪B))=P((A∩B')∩(A∪B))/P(A∪B)
P((A∩B')∩(A∪B))=P(A∩B')*P(A∪B)
P(A∩B')=P(A)*P(B')=0.2*0.5=0.10
P((A∩B')∩(A∪B))=0.1*0.6=0.06
P((A∩B')/(A∪B))=0.06/0.6=0.1
