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

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

Then

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

$=0.70+0.40-0.80=0.30$

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

$=1-0.80=0.20$