Question

The probability that an American company will open a location in Shanghai, China is 0.7. The probability that it will open a location in Beijing, China is 0.4. The probability that it will open a location in either Shanghai or Beijing or both is 0.8. What is the probability that the company will open a location in:
(a) both Shanghai and Beijing?
(b) neither Shanghai nor Beijing?
(c) Beijing but not in Shanghai?
(d) Shanghai given that it opens a location in Beijing?

Answer 1

Answer:

Step-by-step explanation:

Given that the probability that an American company will open a location in Shanghai, China is 0.7.

The probability that it will open a location in Beijing, China is 0.4.

The probability that it will open a location in either Shanghai or Beijing or both is 0.8.

the probability that the company will open a location in:

(a) both Shanghai and Beijing :

$0.7+0.4-P(both)=0.8$

P(both) = 0.3

(using addition theory of probability for union of sets)

(b) neither Shanghai nor Beijing

= 1- P(AUB)

$=1-0.8 = 0.2$

(c) Beijing but not in Shanghai?

P(Beiging)_P(both) = $0.4-0.3=0.1$

(d) Shanghai given that it opens a location in Beijing

=P(Both)/P(Beijing) = $\frac{0.3}{0.4} =0.75$