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 independent not independent

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 value where "Blond" and "Jr" intersect) and \( P(F)=50\% \) (total for "Jr"). So \( P(E|F)=\frac{30}{50}=0.6 = 60\% \).

Step2: Calculate \( P(E) \)

\( P(E) \) is the total for "Blond" divided by the grand - total. \( P(E)=\frac{60}{100}=0.6 = 60\% \)

Step3: Check for independence

Two events \( E \) and \( F \) are independent if \( P(E|F)=P(E) \). Since \( P(E|F) = 60\% \) and \( P(E)=60\% \), the equality holds.

Answer:

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