Question

The probability that Intel will locate in Shanghai, China, is 0.4, the probability that it will locate in Beijing, China, is 0.5, and the probability that it will locate in either Shanghai or Beijing or both is 0.7. Answer the following (a) Let S Shanghai and B-Beijing. From the statement above, list ALL of the probabilities that are given. Example: What is P(B)? (b) What is the probability that Intel will locate in both cities? (c) What is the probability that Intel will locate in neither city?

Answer 1

Let
P(S) denote probability of Intel in Shanghai
P(B) denote probability of Intel in Beijing
$P(S \cup B)$denote the probablity that it is located either Berlin or Munich or both

We are given

P(S)= 0.4
P(B) = 0.5
$P(S \cup B)=0.7$

We know

$P(S \cup B)= P(S)+P(B)-P(S \cap B)\\ 0.7 = 0.4 + 0.5 - P(S \cap B)\\ P(S \cap B)= 0.2$

Probability that the industry will be located in both cities is = 0.2

Probability that the industry is located in neither city

$P(S \cup B)' = 1 -P(S \cup B) = 1 - 0.7 = 0.3$