In a major midwestern university,55 percent of all undergraduates are female,25 percent of all undergraduates belong to a Greek organization (fraternity or sorority),and 40 percent of all males belong to a Greek organization.Are the events "female/male" and "belongs to a Greek organization" independent?
A)Yes,independent
B)No,not independent
$\mathrm{P}(\mathrm{G} \mid \mathrm{F})=.07 / .55=.127 \neq \mathrm{P}(\mathrm{G})$

Question

Quizplus · Accepted Answer

The events are not independent because the probability of belonging to a Greek organization is different for males and females. We can see this by calculating the conditional probabilities:

P(Greek organization | Female) = 0.07/0.55 = 0.127

P(Greek organization | Male) = 0.40

Since these probabilities are not equal, the events are not independent.

In a Major Midwestern University,55 Percent of All Undergraduates Are P(G∣F)=.07/.55=.127≠P(G)\mathrm{P}(\mathrm{G} \mid \mathrm{F})=.07 / .55=.127 \neq \mathrm{P}(\mathrm{G})P(G∣F)=.07/.55=.127=P(G)

In a Major Midwestern University,55 Percent of All Undergraduates Are $\mathrm{P}(\mathrm{G} \mid \mathrm{F})=.07 / .55=.127 \neq \mathrm{P}(\mathrm{G})$