Question

determining if two events are independent

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) = \text{___}\\%\\)
\\(p(e) = \text{___}\\%\\)
events e and f are select

Explanation:

Find the conditional probability \(P(E|F)\)

Using the Conditional Probability Calculation and Two-Way Frequency Tables knowledge points

$$ P(E|F) = \frac{P(E \cap F)}{P(F)} = \frac{30\%}{50\%} = 60\% $$

Find the marginal probability \(P(E)\)

Using the Two-Way Frequency Tables knowledge point

$$ P(E) = 60\% $$

Determine independence of events E and F

Using the Independent Events knowledge point

$$
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$$

Answer:

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?

\(P(E|F) =\) <blank>60</blank>%
\(P(E) =\) <blank>60</blank>%
Events \(E\) and \(F\) are <blank>independent</blank>