Question

QUESTION 3 The probability that an American industry will locate in Berlin is 0.7, the probability that it will locate in Munich is 0.4, and the probability that it will locate in either Berlin or Munich or both is 0.8. What is the probability that the industry will locate in both cities? a. 0.2 b.0.8 О с. 0.4 d.0.3 QUESTION 4 The probability that an American industry will locate in Berlin is 0.7, the probability that it will locate in Munich is 0.4, and the probability that it will locate in either Berlin or Munich or both is 0.8. What is the probability that the industry will locate in neither city? O a. 0.1 b. 0.2 О с. 0.4 d.0.3 al.

Answer 1

Question 3
Let
P(B) denote probability of american industry in Berlin
P(M) denote probability of american industry in Munich
P(B cup M) denote the probablity that it is located either Berlin or Munich or both

We are given

$\\P(B)= 0.7\\ P(M) = 0.4\\ P(B \cup M)=0.8\\$

We know

$\\P(B \cup M)= P(B)+P(M)+P(B \cap M)\\ 0.8 = 0.7 + 0.4 - P(B \cap M)\\ P(B \cap M)= 0.3$

Probability that the industry will be located in both cities is = 0.3 ( Option d= 0.03)

Question 4
Probability that the industry is located in neither city

$P(B \cup M)' = 1 -P(B \cup M) = 1 - 0.08 = 0.02$