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. a student is randomly selected. based on the data, what conclusions can be drawn? p(boy) = p(boy|indoor recess) = the events of the student being a boy and the student preferring indoor recess are

Explanation:

Step1: Calculate $P(\text{Boy})$

The total number of students is $240$, and the number of boys is $160$. So $P(\text{Boy})=\frac{\text{Number of Boys}}{\text{Total Number of Students}}=\frac{160}{240}=\frac{2}{3}$.

Step2: Calculate $P(\text{Boy}|\text{Indoor Recess})$

The number of students who prefer indoor - recess is $96$, and the number of boys who prefer indoor - recess is $64$. By the formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$, in the case of frequency data, $P(\text{Boy}|\text{Indoor Recess})=\frac{\text{Number of Boys who prefer Indoor Recess}}{\text{Number of Students who prefer Indoor Recess}}=\frac{64}{96}=\frac{2}{3}$.

Answer:

1. $P(\text{Boy})=\frac{160}{240}=\frac{2}{3}$
2. $P(\text{Boy}|\text{Indoor Recess})=\frac{64}{96}=\frac{2}{3}$