Question

Northlake high scores to lunch. Soon can eat their lunch in the cafeteria or on an outside patio about 35% of students who have first lunch eat outside compare this with a percenta

Answer 1

The proportion of second lunch students who eat outside is more than that for the first lunch students.

Explanation:

The complete question is:

Points Northlake High School has two lunch periods. Students can eat their lunch in the cafeteria or on an outside patio. About 35% of students who have first lunch eat outside. Compare this with the percentage of second-lunch students who eat outside.

Eat Outside Eat Inside Total

First Lunch 0.19 0.35 0.54

Second Lunch 0.22 0.24 0.46

Total 0.41 0.59 1.00

Solution:

The conditional probability of an event B given that another event A has already occurred is:

`P(B|A)=(P(A\cap B))/(P(A))`

The probability of students who have second lunch (S) and eat outside (O) is:

P (S ∩ O) = 0.22

The probability of students who have second lunch (S) is:

P (S) = 0.41

Compute the proportion of student who eats outside given they have second lunch as follows:

`P(O|S)=(P(S\cap O))/(P(S))`

`=(0.22)/(0.41)\\\\=0.536583\\\\\approx 0.54`

The proportion of second lunch students who eat outside is more than that for the first lunch students.