Question

mrs. higgins surveyed her students, asking what their favorite subject is. the results are below.
science facs ela math art phys. ed.
a) what is the favorite subject for mrs. higgins’ class?
b) what is the least favorite subject for mrs. higgins’ class?
c) if you were to choose a student at random from mrs. higgins’ class, what is the probability the student’s favorite subject would be ela?
d) if you were to choose a student at random from mrs. higgins’ class, what is the probability the student’s favorite subject would be art or facs? why?

Explanation:

Step1: Count 'X's for each subject

Science has 8 'X's, FACS has 3 'X's, ELA has 5 'X's, Math has 1 'X', Art has 3 'X's, Phys. Ed. has 8 'X's.

Step2: Find the favorite subject

The subjects with the most 'X's are Science and Phys. Ed. with 8 each. So the favorite subjects are Science and Phys. Ed.

Step3: Find the least - favorite subject

The subject with the least 'X's is Math with 1 'X'. So the least - favorite subject is Math.

Step4: Calculate probability for ELA

The total number of 'X's is \(8 + 3+5 + 1+3 + 8=28\). The probability \(P(ELA)=\frac{5}{28}\).

Step5: Calculate probability for Art or FACS

The number of 'X's for Art is 3 and for FACS is 3. So the number of favorable outcomes for Art or FACS is \(3 + 3=6\). The probability \(P(Art\ or\ FACS)=\frac{6}{28}=\frac{3}{14}\). The reason is we use the addition rule for mutually - exclusive events (a student can't have two favorite subjects simultaneously in this context), and we sum the number of students who like Art and FACS and divide by the total number of students.

Answer:

a) Science and Phys. Ed.
b) Math
c) \(\frac{5}{28}\)
d) \(\frac{3}{14}\), because we sum the number of students who like Art and FACS and divide by the total number of students.