Answer:
a) P(B^c)=0.8
b) P(A∪B)=0.84
c) P=0.762
Step-by-step explanation:
Let A be the event that the Asian project is successful and B be the event that the European project is successful.
We know that A and B are independent events with probability
P(A) = 0.8
P(B) = 0.2
We know that
P(A∩B)=P(A)·P(B)=0.8·0.2=0.16
a) We know that A and B are independent events, we get
P(B^c)=1-P(B)=1-0.2=0.8
P(B^c)=0.8
b) P(A∪B)=P(A)+P(B)-P(A∩B)
P(A∪B)=0.8+0.2-0.16
P(A∪B)=0.84
The probability that at least one of the two projects will be successful is P(A∪B)=0.84
c) If at least one of the two projects is successful, what is the probability that only the Asian project is successful. We calculate probability
P=\frac{P(A)-P(A∩B)}{ P(A∪B)}
P=(0.8-0.16)/0.84
P=0.64/0.84
P=0.762
