Provide a written description of the complement of the given event.
-The table below describes the smoking habits of a group of asthma sufferers. $\begin{array}{r|cccc}
&& \text {light}& \text {heavy}\
& \text { Nonsmoker } & \text { smoker } & \text {smoker } & \text { Total } \
\hline \text { Men } & 417 & 34 & 31 & 482 \
\text { Women } & 367 & 45 & 47 & 459 \
\text { Total } & 784 & 79 & 78 & 941
\end{array}$
If two different people are randomly selected from the 941 subjects, find the probability that they are both wome:
A) $0.2377$
B) $0.2379$
C) $0.1521$
D) $0.000004747$

Question

Provide a written description of the complement of the given event.
-The table below describes the smoking habits of a group of asthma sufferers. $\begin{array}{r|cccc} 
&& \text {light}& \text {heavy}\
& \text { Nonsmoker } & \text { smoker  } & \text {smoker } & \text { Total } \
\hline \text { Men } & 417 & 34 & 31 & 482 \
\text { Women } & 367 & 45 & 47 & 459 \
\text { Total } & 784 & 79 & 78 & 941
\end{array}$
If two different people are randomly selected from the 941 subjects, find the probability that they are both wome:
A) $0.2377$
B) $0.2379$
C) $0.1521$
D) $0.000004747$

Quizplus · Accepted Answer

The complement of the event "both are women" is "at least one is not a woman". The probability of this event is 1 minus the probability of the event "both are women". The probability of the event "both are women" is:$$P(	ext{both are women}) = \frac{459}{941} 	imes \frac{458}{940} = 0.2377$$Therefore, the probability of the complement of the event "both are women" is:$$P(	ext{at least one is not a woman}) = 1 - 0.2377 = 0.7623$$

Provide a Written Description of the Complement of the Given