Question

the two - way table displays the hair color of the sophomore (so), junior (jr), and senior (sr) classes at west coast high school, represented by percents in the table. let e be the event that the student is blond, and let f be the event that the student is a junior. are events e and f independent? p(e|f)= p(e)= events e and f are

Explanation:

Step1: Calculate \(P(E|F)\)

The formula for conditional probability is \(P(E|F)=\frac{P(E\cap F)}{P(F)}\). From the table, \(P(E\cap F) = 30\%\) (the number of junior - blond students) and \(P(F)=50\%\) (total number of juniors). So \(P(E|F)=\frac{30}{50}=0.6 = 60\%\).

Step2: Calculate \(P(E)\)

\(P(E)\) is the probability that a student is blond. Using the total row, \(P(E)=\frac{60}{100}=0.6=60\%\)

Answer:

\(P(E|F) = 60\%\), \(P(E)=60\%\), Events \(E\) and \(F\) are independent.