Question

Alejandro surveyed his classmates to determine who has ever gone surfing and who has ever gone snowboarding. Let A be the event that the person has gone surfing, and let B be the event that the person has gone snowboarding.

A 4-column table has 3 rows. The first column has entries has surfed, never surfed, total. The second column is labeled has snowboarded with entries 36, 12, 48. The third column is labeled never snowboarded with entries 189, 63, 252. The fourth column is labeled total with entries 225, 75, 300.

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

A and B are independent events because P(A∣B) = P(A) = 0.16.
A and B are independent events because P(A∣B) = P(A) = 0.75.
A and B are not independent events because P(A∣B) = 0.16 and P(A) = 0.75.
A and B are not independent events because P(A∣B) = 0.75 and P(A) = 0.16.

Answer 1

P(A) = 225/300 = 0.75.
P(A|B) = 36/48 = 0.75.
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) = 0.75."