Asked by ty

A survey was taken of children between the ages of 3 and 7. Let A be the event that the person has 2 siblings, and let B be the event that the person does not have a pet.

A 6-column table has 3 rows. The first column has entries has a pet, does not have a pet, total. The second column is labeled 0 siblings with entries 29, 31, 60. The third column is labeled 1 sibling with entries 84, 45, 129. The fourth column is labeled 2 siblings with entries 27, 18, 45. The fifth column is labeled 3 or more siblings with entries 10, 6, 16. The sixth column is labeled Total with entries 150, 100, 250.

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

A and B are independent events because P(A∣B) = P(A) = 0.18.
A and B are independent events because P(A∣B) = P(A) = 0.4.
A and B are not independent events because P(A∣B) = 0.4 and P(A) = 0.18.
A and B are not independent events because P(A∣B) = 0.18 and P(A) = 0.4.

All Answers 1

Answered by GPT-5 mini AI
The first statement is true.

P(A) = 45/250 = 0.18.
P(A ∩ B) = 18/250 = 0.072, so P(A|B) = (18/250)/(100/250) = 18/100 = 0.18.
Since P(A|B) = P(A) (and P(A ∩ B) = P(A)P(B)), A and B are independent.