Question

A survey was taken of children between the ages of 7 and 12. Let A be the event that the person rides the bus to school, and let B be the event that the person has 3 or more siblings.

A 6-column table has 5 rows. The first column has entries walks to school, bikes to school, rides bus to school, driven to school, total. The second column is labeled 0 siblings with entries 24, 8, 18, 32, 82. The third column is labeled 1 sibling with entries 37, 9, 36, 58, 140. The fourth column is labeled 2 siblings with entries 12, 8, 12, 22, 54. The fifth column is labeled 3 or more siblings with entries 3, 2, 9, 10, 24. The sixth column is labeled Total with entries 76, 27, 75, 122, 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) = 0.12.
A and B are independent events because P(A∣B) = P(A) = 0.25.
A and B are not independent events because P(A∣B) = 0.12 and P(A) = 0.25.
A and B are not independent events because P(A∣B) = 0.375 and P(A) = 0.25.

Answer 1

D

Explanation:

A and B are not independent events because P(A∣B) = 0.375 and P(A) = 0.25.

Answer 2

The statement that is true about whether A and B are independent events is D. A and B are not independent events because P(A∣B) = 0.375 and P(A) = 0.25.

How to depict the events?

Let A be the event that the person rides the bus to school, then:

P(A) = 75/300

P(A) = 0.25

Let B be the event that the person has 3 or more siblings, then:

P(B) = 24/300 = 0.25

P(A/B)=9/24

P(A/B)=0.375

Since P(A/B)=0.375 is different from P(A)=0.25 the events are not independent.

Explanation: