Question

select the correct answer from each drop - down menu. a survey asking about preference for recess location was randomly given to students in an elementary school. the results are recorded in the table below.

	indoor recess	outdoor recess	total
boys	64	96	160
girls	32	48	80
total	96	144	240

a student is randomly selected. based on the data, what conclusions can be drawn? $p(\text{boy}) = $ $p(\text{boy}|\text{indoor recess}) = $ the events student being a boy and the student preferring indoor recess are . (drop - down options for $p(\text{boy}|\text{indoor recess})$: 0.67, 0.75, 0.50)

Explanation:

Step1: Calculate P(Boy)

Divide total boys by total students.
$P(\text{Boy}) = \frac{160}{240} = \frac{2}{3} \approx 0.67$

Step2: Calculate P(Boy|Indoor Recess)

Divide boys who prefer indoor recess by total indoor recess students.
$P(\text{Boy}|\text{Indoor Recess}) = \frac{64}{96} = \frac{2}{3} \approx 0.67$

Step3: Check event independence

Compare $P(\text{Boy})$ and $P(\text{Boy}|\text{Indoor Recess})$. Since $P(\text{Boy}) = P(\text{Boy}|\text{Indoor Recess})$, the events are independent.

Answer:

$P(\text{Boy}) = 0.67$
$P(\text{Boy}|\text{Indoor Recess}) = 0.67$
The events "student being a boy and the student preferring indoor recess are independent"