Answer to Question #235674 in Statistics and Probability for Usman

Question

 The probability that an American industry will locate in Shanghai, China, is 0.7, the probability that it will locate in Beijing, China, is 0.4, and the probability that it will locate in either Shanghai or Beijing or both is 0.8. What is the probability that the industry will locate 

i. in both cities?

ii. in neither city?

Answer 1

P(Shanghai) = 0.7

P(Beijing) = 0.4

P(either Shanghai or Beijing) = 0.8

i.

P(A or B) = P(A) + P(B) - P(A and B)

P(A and B) = P(A) + P(B) - P(A and B)

P(both cities) = P(Shanghai and Beijing)

P(Shanghai and Beijing) = P(Shanghai) + P(Beijing) - P(Shanghai or Beijing)

= 0.7 + 0.4 - 0.8

= 0.3

P(Shanghai and Beijing) = 0.3

ii.

P(neither city) = 1 - P(either city)

= 1 - 0.8

= 0.2

P(neither city) = 0.2