The probability that an american industry will locate in shanghai, china, is 0.7, the probability that / / 60 chapter 2 probability 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 (a) in both cities? (b) in neither city?

A) 0.3

B) 0.2

Step-by-step explanation:

We are given the following in the question:

P(Industry in Shanghai) = P(A) = 0.7

P(Industry in Beijing) = P(B) = 0.4

P(Industry in Shanghai or Beijing)  = P(A∪B) = 0.8

a)We need to find the probability that the industry is located in both Shanghai and Beijing that is we need to find P(A∩B)

Formula:

P(A∪B) = P(A) + P(B) - P(A∩B)

Putting the values we get,

0.8 = 0.7 + 0.4 - P(A∩B)

P(A∩B) = 0.3

Thus, the probability that the industry is located in both Shanghai and Beijing is 0.3.

b)Now, we need to find the probability that it is not in either cities

Probability = 1 - Probability(Industry in Shanghai or in Beijing)

                 = 1 - P(A∪B)

                 = 1 - 0.8

                 = 0.2

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.