Answer to Question #299940 in Statistics and Probability for symon

Question

The probability that an American industry will locate in Shanghai China is 0.70, in Beijing is 0.40 and in either Shanghai or Beijing or both is 0.80. what is the probability that the industry will locate : a) in both cities, b) in neither city

Answer 1

$$P(B)=0.70, P(S)=0.40, P(B\cup S)=0.80$$

Then

$$P(both)=P(B\cap S)=P(B)+P(S)-P(B\cup S)$$

$$=0.70+0.40-0.80=0.30$$

$$P(neither\ city)=1-P(B\cup S)$$

$$=1-0.80=0.20$$