Answer:
The events being a heavy smoker and having emphysema are not independent.
Step-by-step explanation:
We are given the following in the question:
Number of women = 2000
Number of heavy smoker = 340
Number of women who has emphysema = 25
Number of women who has emphysema and are heavy smoker = 21
P(Smoker) =
![P(S) = \dfrac{340}{2000}=0.17](https://tex.z-dn.net/?f=P%28S%29%20%3D%20%5Cdfrac%7B340%7D%7B2000%7D%3D0.17)
P(emphysema) =
![P(E) = \dfrac{25}{2000}= 0.0125](https://tex.z-dn.net/?f=P%28E%29%20%3D%20%5Cdfrac%7B25%7D%7B2000%7D%3D%200.0125)
P(Smoker and emphysema) =
![P(S\cap E) = \dfrac{21}{2000} = 0.0105](https://tex.z-dn.net/?f=P%28S%5Ccap%20E%29%20%3D%20%5Cdfrac%7B21%7D%7B2000%7D%20%3D%200.0105)
Two events A and B are said to be independent if
![P(A\cap B)=P(A)\times P(B)](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%29%3DP%28A%29%5Ctimes%20P%28B%29)
Checking conditions for independence:
![P(S)\times P(E) = 0.17\times 0.0125=0.002125\\P(S)\times P(E) \neq 0.0105\\P(S)\times P(E)\neq P(S\cap E)](https://tex.z-dn.net/?f=P%28S%29%5Ctimes%20P%28E%29%20%3D%200.17%5Ctimes%200.0125%3D0.002125%5C%5CP%28S%29%5Ctimes%20P%28E%29%20%5Cneq%200.0105%5C%5CP%28S%29%5Ctimes%20P%28E%29%5Cneq%20P%28S%5Ccap%20E%29)
Thus, the events being a heavy smoker and having emphysema are not independent.
Assuming T, B and N are all on the same line, then we can say
BT + TN = BN
which is the segment addition postulate.
Subtract TN from both sides to get
BT + TN = BN
BT + TN - TN = BN - TN
BT = BN - TN
BN - TN = BT
Which is what choice C is saying. Therefore the answer is choice C.
62+92 is 154. 180- 154 is 26