Question

For the lunch special at a high school cafeteria, students can get either salad or french fries as a side order. The following table shows the number of each side order for the lunch specials purchased on one day, classified by the grade of the student

Grade 9
Grade 10
Grade 11
Grade 12
Total
Salad
37
34
21
28
120
83
71
57
37
248
French fries
Total
120
105
78
65
368

From those who purchased the lunch special that day, one student will be selected at random. What is the probability that the student selected will be in grade 10 given that the student ordered
french fries as the side order?
A
71/368
B
105/368
C
71/245
D
245/308

Answer 1

C 71/248

Explanation:

College Board

Answer 2

The probability that the selected student is in Grade 10 given that they ordered french fries is 105/368.

To find the probability that the selected student is in Grade 10 given that they ordered french fries, we use the conditional probability formula:

Probability(Grade 10 | French fries) = Probability(Grade 10 and French fries) / Probability(French fries)

Find Probability(Grade 10 and French fries):

Probability(Grade 10 and French fries) = 105/368 (number of Grade 10 students who ordered french fries)

Find Probability(French fries):

Probability(French fries) = 368/Total (total number of students who ordered lunch specials)

Substitute the values into the conditional probability formula:

Probability(Grade 10 | French fries) = (105/368) / (368/Total)

Now, compute the expression and simplify if possible.

Probability(Grade 10 | French fries) = 105/368