Answer :
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
[tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]
P(Smoker) =
[tex]P(S) = \dfrac{340}{2000}=0.17[/tex]
P(emphysema) =
[tex]P(E) = \dfrac{25}{2000}= 0.0125[/tex]
P(Smoker and emphysema) =
[tex]P(S\cap E) = \dfrac{21}{2000} = 0.0105[/tex]
Two events A and B are said to be independent if
[tex]P(A\cap B)=P(A)\times P(B)[/tex]
Checking conditions for independence:
[tex]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)[/tex]
Thus, the events being a heavy smoker and having emphysema are not independent.