Question

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.

	0 siblings	1 sibling	2 siblings	3 or more siblings	total
does not have a pet	31	45	18	6	100
total	60	129	45	16	250

which statement is true about whether a and b are independent events?

• a and b are independent events because ( p(a mid b) = p(a) = 0.18 ).
• a and b are independent events because ( p(a mid b) = p(a) = 0.4 ).
• a and b are not independent events because ( p(a mid b) = 0.4 ) and ( p(a) = 0.18 ).
• a and b are not independent events because ( p(a mid b) = 0.18 ) and ( p(a) = 0.4 ).

Explanation:

Step1: Calculate P(A)

$P(A) = \frac{\text{Total with 2 siblings}}{\text{Total surveyed}} = \frac{45}{250} = 0.18$

Step2: Calculate P(A|B)

$P(A|B) = \frac{\text{2 siblings and no pet}}{\text{Total no pet}} = \frac{18}{100} = 0.18$

Step3: Compare P(A|B) and P(A)

Two events are independent if $P(A|B) = P(A)$. Here, both equal 0.18.

Answer:

A. A and B are independent events because P(A | B) = P(A) = 0.18.