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. A 5-column table has 3 rows. The first column has entries Blonde, brown, total. The second column is labeled Sophomore with entries 10, 10, 20. The third column is labeled Junior with entries 30, 20, 50. The fourth column is labeled Senior with entries 20, 10, 30. The fifth column is labeled Total with entries 60, 40, 100. 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

Answer 1

The events E (being blond) and F (being a junior) are not independent because P(E|F) = 30% does not equal P(E) = 60%.

Step-by-step explanation:

To determine whether the events E (being blond) and F (being a junior) are independent, we compare the probability of E given F, denoted as P(E|F), to the probability of E. If P(E|F) is equal to P(E), the two events are independent. Using the table, we first calculate P(E|F). Since 30% of juniors are blond, we have P(E|F) = 30%. Next, we determine P(E) by looking at the total percentage of students who are blond, which is 60%. Now, we compare P(E|F) with P(E).

If the events were independent, the probability of a student being blond should not change based on whether they are a junior. However, since P(E|F) = 30% which is different from P(E) = 60%, events E and F are not independent.

Answer 2

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

Step-by-step explanation:

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