Question

Belleville High School offers classes on three different foreign languages. Let A be the event that a student is in eleventh grade, and let B be the event that a student is enrolled in French class.

A 5-column table has 4 rows. The first column has entries Tenth grade, eleventh grade, twelfth grade, total. The second column is labeled Spanish with entries 107, 56, 89, 252. The third column is labeled French with entries 122, 68, 82, 272. The fourth column is labeled German with entries 6, 14, 8, 28. The fifth column is labeled Total with entries 235, 138, 179, 552.

Which statement is true about whether A and B are independent events?

A and B are independent events because P(A∣B) = P(A).
A and B are independent events because P(A∣B) = P(B).
A and B are not independent events because P(A∣B) ≠ P(A).
A and B are not independent events because P(A∣B) ≠ P(B).

Answer 1

Compute the probabilities from the table:

- P(A) = P(eleventh grade) = 138/552 = 0.25.
- P(B) = P(French) = 272/552 ≈ 0.4928.
- P(A|B) = P(eleventh grade | French) = 68/272 = 0.25.

Since P(A|B) = P(A), A and B are independent.

So the correct statement is: "A and B are independent events because P(A∣B) = P(A)."