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?
$p(\text{boy}) = 0.67$
$p(\text{boy}|\text{indoor recess}) = $
the events of the student being a boy and the student preferring indoor recess are
(options in drop - down: 0.50, 0.75, 0.67)

Explanation:

Step1: Calculate P(Boy|Indoor Recess)

Conditional probability formula: $P(Boy|Indoor\ Recess) = \frac{\text{Number of boys who prefer indoor recess}}{\text{Total number of students who prefer indoor recess}}$
$\frac{64}{96} = \frac{2}{3} \approx 0.67$

Step2: Check event independence

Two events A (being a boy) and B (preferring indoor recess) are independent if $P(A|B) = P(A)$.
We have $P(Boy) \approx 0.67$ and $P(Boy|Indoor\ Recess) \approx 0.67$, so $P(Boy|Indoor\ Recess) = P(Boy)$.

Answer:

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