Question

it will locate in beijing, china, is 0.4, and the proba- bility that it will locate in either shanghai or beijing or both is 0.8. what is the probability that the industry will locate (a) in both cities? (b) in neither city?

Answer 1

The probability that the industry will locate in both cities is 0.4. The probability that it will locate in either Shanghai or Beijing or both is 0.8.

Explanation:

The probability that the industry will locate in both cities is 0.41. The probability that it will locate in either Shanghai or Beijing or both is 0.81. We can use the formula P(A and B) = P(A) * P(B|A) to calculate the probability of an event occurring in both cities. Let A be the event that the industry locates in Beijing and B be the event that it locates in Shanghai. Then, P(A or B) = P(A) + P(B) - P(A and B) = 0.8. Therefore, P(A and B) = P(A) * P(B|A) = (0.4 * 0.4)/0.8 = 0.2. The probability that the industry will not locate in either city is given by P(neither A nor B) = 1 - (P(A) + P(B) - P(A and B)) = 1 - (0.4 + 0.4 - 0.2) = 0.2.

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